Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Qualitative methods in bifurcation theory

Author: Jerrold E. Marsden
Journal: Bull. Amer. Math. Soc. 84 (1978), 1125-1148
MSC (1970): Primary 35B30, 57D45, 73G05, 83C05
MathSciNet review: 508450
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • R. Abraham and J. Marsden [1978], Foundations of mechanics, 2nd ed., Benjamin, New York. MR 515141
  • J. C. Alexander and J. A. Yorke [1978], Global bifurcation of periodic orbits, Amer. J. Math, (to appear). MR 474406
  • S. S. Antman [1977], Bifurcation problems for nonlinearly elastic structures, Applications of Bifurcation Theory, P. A. Rabinowitz (ed.), Academic Press, New York, pp. 73-126. MR 459178
  • S. S. Antman and K. B. Jordan [1974], Qualitative aspects of the spatial deformation of non-linearly elastic rods, Proc. Roy. Soc. Edinburgh Sect. A 73, 85-105. MR 408386
  • S. S. Antman and E. R. Carbone [1977], Shear and necking instabilities in nonlinear elasticity, J. Elasticity 7, 125-152. MR 451990
  • S. S. Antman and G. Rosenfeld [1978], Global behavior of buckled states of nonlinearly elastic rods, SIAM Rev. (to appear). MR 495396
  • J. Arms and J. Marsden [1978], On the sufficiency of Killing fields for linearization instability in general relativity, Indiana Univ. Math. J. (to appear). MR 523627
  • V. Arnold [1972], Bifurcations in versal families, Russian Math. Surveys 27, 54-123. MR 413191
  • J. M. Ball [1974], Saddle point analysis for an ordinary differential equation in a Banach space and an application to dynamic buckling of a beam, Nonlinear Elasticity, J. Dickey (ed.), Academic Press, New York.
  • S. Bancroft, J. K. Hale and D. Sweet [1968], Alternative problems for nonlinear functional equations, J. Differential Equations 4, 40-68. MR 220118
  • L. Bauer and E. L. Reiss [1965], Nonlinear buckling of rectangular plates, SIAM Rev. 13, 603-626.
  • L. Bauer, E. Reiss and H. Keller [1975], Multiple eigenvalues lead to secondary bifurcations, SIAM Rev. 17, 101-122. MR 378546
  • T. Brook Benjamin [1961], Dynamics of a system of articulated pipes conveying fluid, Proc. Roy. Soc. London Ser. A 261, 457-499. MR 122199
  • T. Brook Benjamin, [1976], The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics, Lecture Notes in Math., vol. 503, Springer-Verlag, Berlin and New York, pp. 8-29. MR 671099
  • T. Brook Benjamin, [1977], Bifurcation phenomena in steady flows of a viscous fluid (preprint).
  • M. S. Berger [1973], Applications of global analysis to specific nonlinear eigenvalue problems, Rocky Mountain J. Math. 3, 319-354. MR 328691
  • M. S. Berger and P. C. Fife [1967], On von Karman's equations and the buckling of a thin elastic plate, Comm. Pure Appl. Math. 20, 687-719; 21, 227-241. MR 221808
  • J. Boa and D. S. Cohen [1976], Bifurcation of localized disturbances in a model biochemical reaction, SIAM J. Appl. Math. 30, 123-135.
  • M. Buchner, J. Marsden and S. Schecter [1978], A differential topology approach to bifurcation at multiple eigenvalues (to appear).
  • G. Capriz and P. P. Guidugli [1974], On Signorini's perturbation method in finite elasticity. Arch. Rational Mech. Anal. 57, 1-30. MR 368543
  • L. Cesari [1976], Functional analysis, nonlinear differential equations and the alternative method, Nonlinear functional analysis and differential equations, L. Cesari, R. Kannan and J. Schuur (eds.), Marcel Dekker, New York. MR 487630
  • D. Chillingworth [1975], The catastrophe of a buckling beam, Dynamical systems, Lecture Notes in Math., vol. 488, Springer-Verlag, Berlin and New York, pp. 88-91.
  • D. Chillingworth, [1976], Differential topology with a view of applications, Pitman, New York. MR 646088
  • D. Chillingworth and J. Marsden [1978], Bifurcations near equilibrium for the traction problem in nonlinear elastostatics (in preparation).
  • S. Chow, J. Hale and J. Mallet-Paret [1975], Applications of generic bifurcation, I, Arch. Rational Mech. Anal. 59, 159-188. MR 390852
  • S. Chow, J. Hale and J. Mallet-Paret, [1976], Applications of generic bifurcation. II, Arch. Rational Mech. Anal. 62, 209-236. MR 415673
  • S. Chow and J. Mallet-Paret [1978], Fuller index and global Hopf bifurcation, J. Differential Equations (to appear). MR 492560
  • S. N. Chow, J. Mallet-Paret and J. A. Yorke [1978], Global Hopf bifurcation from a multiple eigenvalue (preprint). MR 512165
  • D. S. Cohen, [1973], Multiple solutions of nonlinear partial differential equations, Lecture Notes in Math., vol. 322, Springer-Verlag, Berlin and New York, pp. 15-77. MR 371548
  • D. S. Cohen, [1977], Bifurcation from multiple complex eigenvalues, J. Math. Anal. Appl. 57, 505-521. MR 425267
  • M. Crandall and P. Rabinowitz [1971], Bifurcation from simple eigenvalues, J. Functional Analysis 8, 321-340. MR 288640
  • M. Crandall and P. Rabinowitz, [1973], Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal. 52, 161-180. MR 341212
  • E. Dancer [1971], Bifurcation theory in real Banach spaces, Proc. London Math. Soc. 23, 699-734; 26 (1973), 359-384; 27 (1973), 747-765. MR 305166
  • E. Dancer, [1973], Global solution branches for positive mappings, Arch. Rational Mech. Anal. 52, 181-192. MR 353077
  • R. W. Dickey [1973], Dynamic stability of equilibrium states of the extensible beam, Proc. Amer. Math. Soc. 41, 94-102. MR 328290
  • R. W. Dickey, [1976], Bifurcation problems in nonlinear elasticity, Research Notes in Mathematics, no. 3, Pitman, New York. MR 489173
  • E. H. Dowell [1966], Nonlinear oscillations of a fluttering plate, AIAA J., vol. 4, 1267-1275.
  • E. H. Dowell, [1975], Aeroelasticity of plates and shells, Noordhoff, Groningen.
  • J. J. Duistermaat [1974], Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math. 27, 207-281. MR 405513
  • E. R. Fadell and P. H. Rabinowitz [1977], Bifurcation for odd potential operators and an alternative topological index, J. Functional Analysis 26, 48-67. MR 448409
  • A. Fischer and J. Marsden [1975a], Linearization stability of nonlinear partial differential equations, Proc. Sympos. Pure Math., vol. 27, part 2, Amer. Math. Soc., Providence, R. I., pp. 219-263. MR 383456
  • A. Fischer and J. Marsden, [1975b], Deformations of the scalar curvature, Duke Math. J. 42, 519-547. MR 380907
  • A. Fischer, J. Marsden and V. Moncrief [1978], Linearization stability of the Einstein equations (in preparation).
  • C. Foiaş and R. Temam [1977], On generic finiteness of solutions of the stationary Navier-Stokes equations, Comm. Pure Appl. Math. 30, 149-164. MR 435626
  • M. Golubitsky and V. Guillemin [1973], Stable mappings and their singularities, Springer-Verlag, Berlin and New York. MR 341518
  • M. Golubitsky [1978], An introduction to catastrophe theory and its applications, SIAM Rev. 28, 352-387. MR 470984
  • M. Golubitsky and D. Schaeffer [1978], A theory for imperfect bifurcation via singularity theory (preprint). MR 508917
  • W. M. Greenlee [1973], Remarks on branching from multiple eigenvalues, Lecture Notes in Math., vol. 322, Springer-Verlag, Berlin and New York, pp. 101-112.
  • G. Grioli [1962], Mathematical theory of elastic equilibrium, Ergebnisse der Ang. Mat, no. 7, Springer-Verlag, Berlin and New York.
  • D. Gromoll and W. Meyer [1969], On differentiable functions with isolated critical points, Topology 8, 361-369. MR 246329
  • J. Guckenheimer [1973], Catastrophes and partial differential equations, Ann. Inst Fourier (Grenoble) 23, 31-59. MR 365627
  • M. Gurtin and R. MacCamy [1974], Non-linear age-dependent population dynamics, Arch. Rational Mech. Anal. 54, 281-300. MR 354068
  • G. J. Habetler, and B. J. Matkowsky [1974], On the validity of a nonlinear dynamic stability theory, Arch. Rational Mech. Anal. 57, 166-188. MR 361404
  • J. K. Hale [1963], Oscillations in nonlinear systems, McGraw-Hill, New York. MR 150402
  • J. K. Hale, [1977], Lectures on generic bifurcation theory, Symposium on Nonlinear Analysis and Mechanics, vol. I, R. J. Knops (ed.), Lecture Notes in Math., Pitman, New York. MR 501048
  • J. K. Hale and H. M. Rodrigues [1977], Bifurcation in the Duffing equation with several parameters, Proc. Roy. Soc. Edinburgh (to appear).
  • W. S. Hall [1971], The bifurcation of solutions in Banach spaces, Trans. Amer. Math. Soc. 161, 207-208. MR 282267
  • B. Hassard [1975], Bifurcation of periodic solutions of the Hodgkin-Huxley model for the current-clamped squid giant axon (preprint).
  • B. Hassard and Y. H. Wan [1978], Bifurcation formulae derived from center manifold theory, J. Math. Anal. Appl. (to appear). MR 488152
  • M. Hirsch, C. Pugh, and M. Schub [1977], Invariant manifolds, Lecture Notes in Math., vol. 585, Springer-Verlag, Berlin and New York. MR 501173
  • P. Holmes [1977], Bifurcations to divergence and flutter in flow induced oscillations-a finite dimensional analysis, J. Sound and Vib. 53, 471-503. MR 455875
  • P. J. Holmes [1978], A nonlinear oscillator with a strange attractor (preprint). MR 560797
  • P. Holmes and J. Marsden [1978], Bifurcations to divergence and flutter in flow induced oscillations-an infinite dimensional analysis, Automatica (to appear). MR 534867
  • P. Holmes and J. Marsden, [1979], Qualitative analysis of a class of partial differential equations describing flutter (in preparation).
  • J. Ize [1976], Bifurcation theory for Fredholm operators, Mem. Amer. Math. Soc. No. 174. MR 425696
  • D. Joseph [1976], Stability of fluid motions. I, II, Springer-Verlag, New York. MR 449147
  • J. P. Keener [1974], Perturbed bifurcation theory at multiple eigenvalues, Arch. Rational Mech. Anal. 56, 348-366. MR 355710
  • J. P. Keener and H. B. Keller [1973], Perturbed bifurcation theory, Arch. Rational Mech. Anal. 50, 159-175. MR 336479
  • J. B. Keller and S. Antman [1969], Bifurcation theory and nonlinear eigenvalue problems, Benjamin, New York. MR 241213
  • H. B. Keller and W. F. Langford [1972], Iterations, perturbations and multiplicities for nonlinear bifurcation problems, Arch. Rational Mech. Anal. 48, 83-108. MR 336478
  • H. Kielhofer [1974], Stability and semilinear evolution equations in Hilbert space, Arch. Rational Mech. Anal. 57, 150-165. MR 442405
  • K. Kirchgassner [1971], Multiple eigenvalue bifurcation for holomorphic mappings, Contributions to nonlinear functional analysis, E. H. Zarantello (ed.), Academic Press, New York. MR 399973
  • G. H. Knightly and D. Sather [1970], On nonuniqueness of solutions of the von Kermen equations, Arch. Rational Mech. Anal. 36, 65-78. MR 261835
  • G. H. Knightly and D. Sather, [1974], Nonlinear buckled states of rectangular plates, Arch. Rational Mech. Anal. 54, 356-372. MR 349106
  • G. H. Knightly and D. Sather, [1977], Existence and stability of axisymmetric buckled states of spherical shells, Arch. Rational Mech. Anal. 63, 305-320. MR 436732
  • W. T. Koiter [1963], Elastic stability and post-buckling behavior, Nonlinear problems, R. Langer (ed.), Univ. of Wisconsin Press, Madison, Wis., pp. 257-275. MR 148292
  • W. T. Koiter, [1970], Over de stabiliteit van het elastich evenwicht, Thesis Delft, (1945) Eng. Transl. Tech. Report. AFFDL-TR-70-25.
  • M. A. Krasnosel'skiĭ [1964], Topological methods in the theory of nonlinear integral equations, Pergamon Press, New York, Oxford. MR 159197
  • M. A. Krasnosel'skiĭ, [1971], The projection method for the study of bifurcation of the zero solution of a nonlinear operator equation with multidimensional singularity, Soviet Math. Dokl. 12, 967-971.
  • N. H. Kuiper [1971], Morse relations for curvature and tightness, Proc. Liverpool Singularities Sympos., II, Lecture Notes in Math., vol. 209, Springer-Verlag, Berlin and New York, pp. 77-89. MR 343297
  • K. A. Landman and S. Rosenblat [1978], Bifurcation from a multiple eigenvalue and stability of solutions, SIAM J. Appl. Math. 34, 743-759. MR 477921
  • S. List [1976], Generic bifurcation with application to the von Kármán equations, Thesis, Brown Univ., Providence, R. I.
  • J. MacBain [1974], Global bifurcation for noncompact operators, Bull. Amer. Math. Soc. 80, 1005-1009. MR 361961
  • J. B. McLeod and D. H. Sattinger [1973], Loss of stability and bifurcation at a double eigenvalue, J. Functional Analysis 14, 62-84. MR 353079
  • J. B. McLeod and R. E. L. Turner [1977], Bifurcation for non-differentiable operators with an application to elasticity, Arch. Rational Mech. Anal. 63, 1-46. MR 473953
  • R. J. Magnus [1976], On the local structure of the zero set of a Banach space valued mapping, J. Functional Analysis 22, 58-72. MR 418149
  • R. J. Magnus, [1976b], A generalization of multiplicity and a problem of bifurcation, Proc. London Math. Soc. 32, 251-278. MR 402561
  • R. Magnus and T. Poston [1977], On the full unfolding of the von Kármán equations at a double eigenvalue, Battelle Report # 109.
  • J. Mallet Paret [1977], Buckling of cylindrical shells with small curvature, Quart. Appl. Math. 35, 383-400. MR 478917
  • J. Marsden [1977], Attempts to relate the Navier Stokes equations to turbulence, Seminar on Turbulence, P. Bernard and T. Ratiu (eds.), Lecture Notes in Math., vol. 615, Springer-Verlag, Berlin and New York. MR 482850
  • J. Marsden and T. Hughes [1978], Topics in the mathematical foundations of elasticity, Nonlinear Analysis and Mechanics, vol. II, R. J. Knops (ed.), Pitman, New York. MR 576233
  • J. Marsden and M. McCracken [1976], The Hopf bifurcation and its applications, Applied Math. Sciences, vol. 19, Springer-Verlag, Berlin and New York. MR 494309
  • J. Marsden and A. Tromba [1978], On generic finiteness of solutions of the Navier-Stokes equations (in preparation).
  • B. Matkowsky and L. Putnik [1974], Multiple buckles states of rectangular plates, Internat J. Non-Linear Mech. 9, 89-103.
  • B. J. Matkowski and E. L. Reiss [1977], Singular perturbations of bifurcations, SIAM J. Appl. Math. 33, 230-255. MR 516193
  • E. Mettler [1962], Dynamic buckling, Handbook of Engineering Mechanics, S. Flügge (ed.), McGraw-Hill, New York.
  • J. Milnor [1963], Morse theory, Ann. of Math. Studies, no. 51, Princeton Univ. Press, Princeton, N.J. MR 163331
  • V. Moncrief [1975], Space-time symmetries and linearization stability of the Einstein equations, J. Math. Phys. 16, 493-502; 17, 1893-1902. MR 416469
  • J. Moser [1976], Periodic orbits near an equilibrium and a theorem by Alan Weinstein, Comm. Pure Appl. Math. 29, 727-747. MR 426052
  • L. Nirenberg [1974], Topics in nonlinear analysis, Courant Institute Lecture Notes, New York. MR 488102
  • R. Nussbaum [1978], A Hopf global bifurcation theorem for retarded functional differential equations, Trans. Amer. Math. Soc. 238, 139-164. MR 482913
  • P. C. Parks [1966], A stability criterion for a panel flutter problem via the second method of Liapunov, Differential Equations and Dynamical Systems, J. K. Hale and J. P. LaSalle (eds.), Academic Press, New York.
  • G. H. Pimbley [1969], Eigenfunction branches of nonlinear operators and their bifurcations, Springer-Verlag, Berlin and New York. MR 266007
  • T. Poston and I. Stewart [1978], Catastrophe theory and its applications, Pitman, New York. MR 501079
  • M. Potier-Ferry [1977], Perturbed bifurcation theory (preprint). MR 540820
  • A. J. Pritchard and W. T. F. Blakeley [1976], Perturbation results and their applications to problems in structural dynamics, Lecture Notes in Math., vol. 503, Springer-Verlag, Berlin and New York, pp. 438-449. MR 669236
  • P. H. Rabinowitz [1971], Some global results for nonlinear eigenvalue problems, J. Functional Analysis 7, 487-513. MR 301587
  • P. H. Rabinowitz, [1977], A bifurcation theorem for potential operators, J. Functional Analysis 25, 412-424. MR 463990
  • P. H. Rabinowitz, [1978], Free vibrations for a semilinear wave equation, Comm. Pure. Appl. Math. 31, 31-68. MR 470378
  • D. Rand [1976], Arnold's classification of simple singularities of smooth functions (Warwick preprint).
  • M. Reeken [1973], Stability of critical points under small perturbations, Manuscripta Math. 8, 69-72. MR 331424
  • E. L. Reiss and B. J. Matkowsky [1971], Nonlinear dynamic buckling of a compressed elastic column, Quart Appl. Math. 29, 245-260. MR 286344
  • J. Roorda [1965], Stability of structures with small imperfections, J. Eng. Mech. Div., Proc. Amer. Soc. Engr. 1 (1965), 87-106, 6 (1967), 37-48; J. Mech. Phys. Solids 13 (1965), 267-280; Internat. J. Solids and Structures 4 (1968), 1137-1148.
  • D. Sather [1973], Branching of solutions of nonlinear equations, Rocky Mountain J. Math. 3, 203-250. MR 336484
  • D. Sather, [1976], Branching and stability for nonlinear shells, Lecture Notes in Math., vol. 503, Springer-Verlag, Berlin and New York, pp. 462-473. MR 669237
  • D. Sather, [1977], Bifurcation and stability for a class of shells, Arch. Rational Mech. Anal. 63, 295-304. MR 434079
  • D. Sattinger [1973], Topics in stability and bifurcation theory, Lecture Notes in Math., vol. 309, Springer-Verlag, Berlin and New York. MR 463624
  • D. Sattinger, [1976], Bifurcations, pattern formation and symmetry groups (preprint). MR 467812
  • I. Segal [1962], Nonlinear semigroups, Ann. of Math. (2) 78, 339-364. MR 152908
  • E. Sel'kov [1968], Self-oscillations in glycose, Europ. J. Biochem. 4, 79-86.
  • M. J. Sewell [1966], On the connection between stability and the shape of an equilibrium surface, J. Mech. Phys. Solids 14 203-230.
  • M. J. Sewell, [1969], A method of post buckling analysis, J. Mech. Phys. Solids 17, 219-233.
  • M. J. Sewell, [1976], Some mechanical examples of catastrophe theory, Bull. Inst Math. Appl. 12, 163-172. MR 649268
  • M. J. Sewell, [1978], Degenerate duality, catastrophes and saddle functionals, Ossolineum Publishing House of the Polish Academy (to appear). MR 560096
  • M. Shearer [1976], Bifurcation from a multiple eigenvalue, Ordinary and partial differential equations (Dundee 1976), Lecture Notes in Math., vol. 564, 417-424. Springer-Verlag, Berlin and New York. MR 637089
  • M. Shearer, [1977], Small solutions of a non-linear equation on Banach space for a degenerate case, Proc. Roy Soc. Edinburgh Sect. A, 79, 35-49. MR 477928
  • M. Shearer, [1977], Bifurcation in the neighborhood of a non-isolated singular point (preprint). MR 501095
  • S. Smale [1970], Topology and mechanics, Invent Math. 10, 305-331. MR 309153
  • Stakgold [1971], Branching of solutions of nonlinear equations, SIAM Rev. 13, 289-332. MR 291913
  • F. Stoppelli [1958], Sull'esistenza do soluzioni delle equazioni dell'elastostatica isoterma nel caso di sollecitazioni dotate di assi di equilibrio, Ricerche Mat. 6, 241-287; ibid 7, 71-101, 138-152. MR 101653
  • C. A. Stuart [1973], Some bifurcation theory for k-set contractions, Proc. London Math. Soc. 27, 531-550. MR 333856
  • C. A. Stuart, [1977], Global properties of components of solutions of nonlinear second order ordinary differential equations on the half line, Ann. Scuola Norm. Sup. Pisa (to appear).
  • J. T. Stuart [1571], Nonlinear stability theory, Ann. Rev. Fluid Mech. 3, 347-370.
  • F. Takens [1972], Some remarks on the Böhme-Berger bifurcation Theorem, Math. Z. 129, 359-364. MR 315538
  • F. Takens, [1974a], Singularities of vector fields, Publ. Inst Hautes Études Sci. 43, 47-100. MR 339292
  • F. Takens, [1974b], Forced oscillations, Notes, Utrecht.
  • R. Thorn [1972], Structural stability and morphogenesis, (English transl. by D. Fowler (1975)), Benjamin, New York. MR 488156
  • J. M. T. Thompson and G. W. Hunt [1973], A general theory of elastic stability, Wiley, New York. MR 400868
  • J. M. T. Thompson and G. W. Hunt, [1975], Towards a unified bifurcation theory, Z. Angew. Math. Phys. 26, 581-604. MR 388441
  • J. F. Toland [1977], Global bifurcation theory via Galerkin's method, Nonlinear analysis, Theory, Methods and Appl. 1, 305-317. MR 516195
  • A. J. Tromba [1976a] Almost Riemannian structures on Banach manifolds, the Morse Lemma and the Darboux Theorem, Canad. J. Math. 28, 640-652. MR 402799
  • A. J. Tromba, [1976b], Fredholm vector fields and a transversality theorem, J. Functional Analysis 23, 362-368. MR 438385
  • A. J. Tromba, [1978], A general approach to Morse theory, J. Differential Geometry (to appear); see also On the number of solutions to Plateau's problem, Bull. Amer. Math. Soc. 82 (1976), 66-68 and On the number of simply connected minimal surfaces spanning a curve, Mem. Amer. Math. Soc. No. 194 (1977). MR 464304
  • C. Truesdell and W. Noll [1965], The nonlinear field theories of mechanics, Encyclopedia of Physics, Vol. III, Springer-Verlag, Berlin and New York. MR 1215940
  • R. E. L. Turner [1975], Transversality and cone maps, Arch. Rational Mech. Anal. 58, 151-179. MR 388189
  • K. Uhlenbeck [1975], Generic properties of eigenfunctions, Amer. J. Math. 98, 1059-1078. MR 464332
  • B. T. Ulrich [1975], Josephson junction dynamics from the viewpoint of catastrophe theory, Proc. 14th Internat. Conf. on Low Temp. Phys. (Helsinki, 1975), pp. 222-225.
  • M. M. Vainberg and V. A. Trenogin [1962], The methods of Lyapunov and Schmidt in the theory of nonlinear equations and their further development, Russian Math. Surveys 17, 1-60. MR 154113
  • M. M. Vainberg and V. A. Trenogin, [1974], Theory of branching of solutions of nonlinear equations, Noordhoff, Groningen.
  • W. Van Buren [1968], On the existence and uniqueness of solutions to boundary value problems in finite elasticity, Westinghouse Research Report 68-1D7-MEKMAR1.
  • A. Vanderbauwhede [1977], Generic and non-generic bifurcation for the von Kármán equations, J. Math. Anal. Appl. (to appear). MR 517746
  • Y.-H. Wan [1977], On the uniqueness of invariant manifolds, J. Differential Equations 24, 268-273. MR 455047
  • Y.-H. Wan, [1978], Generic deformations of varieties (preprint). MR 561826
  • C. C. Wang and C. Truesdell [1973], Introduction to rational elasticity, Noordhoof, Groningen. MR 468442
  • G. Wasserman [1974], Stability of unfoldings, Lecture Notes in Math., vol. 393, Springer-Verlag, Berlin and New York. MR 410789
  • A. Weinstein [1978], Bifurcations and Hamilton's principle, Invent. Math, (to appear). MR 501163
  • D. Westreich [1973], Banach space bifurcation theory, Trans. Amer. Math. Soc. 171, 135-156. MR 328706
  • S. Williams [1968], A connection between the Cesari and Leray-Schauder methods, Michigan Math. J. 15, 441-448. MR 236791
  • E. C. Zeeman [1976], Euler buckling, Structural stability, the theory of catastrophes, and applications in the sciences, Lecture Notes in Math., vol. 525, Springer-Verlag, Berlin and New York, pp. 373-395. MR 515875
  • E. C. Zeeman and D. J. A. Trotman [1976], The classification of elementary catastrophes of codimension $łeq 5$, Structural stability, the theory of catastrophes, and applications in the sciences, Lecture Notes in Math., vol. 525, Springer-Verlag, Berlin and New York, pp. 263-327.
  • H. Zeigler [1968], Principles of structural stability, Blaisdell, Waltham, Mass.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 35B30, 57D45, 73G05, 83C05

Retrieve articles in all journals with MSC (1970): 35B30, 57D45, 73G05, 83C05

Additional Information


American Mathematical Society