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Book Review
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Book Information
Author(s):
Svatopluk Fučík
Title:
Solvability of nonlinear equations and boundary value problems
Additional book information:
Mathematics and its Applications, vol. 4, D. Reidel Publishing Company, Dordrecht, Holland/Boston, USA, London, England, 1980, 400 pp., $29.95
References:
- 1.
- S. Ahmad, A. Lazer, and J. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933-944. MR 427825
- 2.
- H. Amann and P. Hess, A multiplicity result for a class of elliptic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), 145-151. MR 549877
- 3.
- H. Amann and E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa 7 (1980), 539-603. MR 600524
- 4.
- A. Ambrosetti and G. Prodi, On the inversion of some differentiate mappings with singularities between Banach spaces, Ann. Mat. Pura Appl. (4) 93 (1972), 231-247. MR 320844
- 5.
- A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional. Anal. 14 (1973), 349-381. MR 370183
- 6.
- A. Ambrosetti and G. Mancini, Sharp nonuniqueness results for some nonlinear problems, Nonlinear Anal. Theory, Applications, Methods 3 (1979), 635-645. MR 541874
- 7.
- A. Bahri and H. Berestycki, A perturbation method in critical point theory and applications, Trans. Amer. Math. Soc. 267 (1981), 1-32. MR 621969
- 8.
- J. Bebernes, R. Gaines, and K. Schmitt, Existence of periodic solutions of third and fourth-order ordinary differential equations via coincidence degree, Ann. Soc. Sci. Bruxelles, Ser. I 88 (1974), 25-36. MR 340729
- 9.
- V. Benci and P. H. Rabinowitz, Critical point theorems for indefinite functionals, Invent. Math. 52 (1979), 241-273. MR 537061
- 10.
- M. S. Berger and E. Podolak, On the solutions of a nonlinear Dirichlet problem, Indiana Univ. Math. J. 24 (1975), 837-846. MR 377274
- 11.
- M. S. Berger, Review of "Nonlinear differential equations", by S. Fučík and A. Kufner, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 362-368.
- 12.
- H. Brezis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa 5 (1978), 225-326. MR 513090
- 13.
- A Castro, A two point boundary value problem with jumping nonlinearities, Proc. Amer. Math. Soc. 79 (1980), 207-211. MR 565340
- 14.
- L. Cesari, Functional analysis and periodic solutions of nonlinear differential equations, Contr. Diff. Equations 1 (1963), 149-187. MR 151678
- 15.
- L. Cesari, Functional analysis and Galerkin's method, Michigan Math. J. 11 (1964), 385-414. MR 173839
- 16.
- C. C. Chang, Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure Appl. Math. 34 (1981), 693-712. MR 622618
- 17.
- S-N. Chow and J. K. Hale, Methods of bifurcation theory, Springer-Verlag, New York, Heidelberg, Berlin, 1982. MR 660633
- 18.
- D. C. Clark, A variant of Lusternik Schnirelman theory, Indiana Univ. Math. J. 22 (1972), 65-74. MR 296777
- 19.
- D. C. Clark, On periodic solutions of autonomous Hamiltonian system of ordinary differential equations, Proc. Amer. Math. Soc. 39 (1973), 579-584. MR 315217
- 20.
- D. G. Costa and J. V. A. Gonçalves, Existence and multiplicity results for a class of nonlinear elliptic boundary value problems at resonance, J. Math. Anal. Appl. 84 (1981), 328-337. MR 639667
- 21.
- E. N. Dancer, On the ranges of certain weakly nonlinear elliptic partial differential equations, J. Math. Pures Appl. 57 (1978), 351-366. MR 524624
- 22.
- E. N. Dancer, Nonuniqueness for nonlinear boundary-value problems (to appear). MR 715763
- 23.
- C. L. Dolph, Nonlinear integral equations of the Hammerstein type, Trans. Amer. Math. Soc. 60 (1949), 289-307. MR 32923
- 24.
- H. Ehrmann, Über die Existenz der Lösungen von Randwertaufgaben bei gewöhnlicher nichtlinear differentialgleichungen zweiter ordnung, Math. Ann. 134 (1957), 167-194. MR 92056
- 25.
- D. G. de Figueiredo and J.-P. Gossez, Nonlinear perturbations of a linear elliptic problem near its first eigenvalue, J. Differential Equations 30 (1978), 1-19. MR 511471
- 26.
- D. G. de Figueiredo and W-M Ni, Perturbations of second order linear elliptic problems by nonlinearities without Landesman-Lazer condition, Nonlinear Analysis, Theory, Applications, Methods 3 (1979), 629-634. MR 541873
- 27.
- S. Fučík, Nonlinear equations with noninvertible linear part, Czechoslovak Math. J. 24 (1974), 259-271. MR 348568
- 28.
- S. Fučík and V. Lovicar, Periodic solutions of the equation x"(t) + g(x(t)) = p(t), Časopis Pest. Mat. 100 (1975), 160-175. MR 385239
- 29.
- S. Fučík, J. Neč, and M. Kučera, Ranges of nonlinear asymptotically linear operators, J. Differential Equations 17 (1975), 375-394. MR 372696
- 30.
- S. Fučík, Boundary value problems with jumping nonlinearities, Časopis. Pěst. Mat. 101 (1976), 69-87. MR 447688
- 31.
- R. E. Gaines and J. L. Mawhin, Coincidence degree and nonlinear differential equations, Lecture Notes in Math., vol. 568, Springer-Verlag, Berlin and New York, 1977. MR 637067
- 32.
- A. Hammerstein, Nichtlineare Integralgleichungen nebst Anwendungen, Acta. Math. 54 (1930), 117-176. MR 1555304
- 33.
- A. Haraux, Nonlinear evolution equations--global behavior of solutions, Lecture Notes in Math., vol 841, Springer-Verlag, Berlin and New York, 1981. MR 610796
- 34.
- J. A. Hemple, Multiple solutions for a class of nonlinear boundary value problems, Indiana Univ. Math. J. 20 (1971), 983-996. MR 279423
- 35.
- H. Hofer, Variational and topological methods in partially ordered Hilbert spaces, Math. Ann. (to appear). MR 682663
- 36.
- J. L. Kazdan and F. Warner, Remarks on quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (1975), 567-597. MR 477445
- 37.
- E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. MR 267269
- 38.
- A. C. Lazer and P. J. McKenna, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl. 84 (1981), 282-294. MR 639539
- 39.
- A. C. Lazer and P. J. McKenna, On a conjecture related to the number of solutions of a nonlinear Dirichlet problem (to appear).
- 40.
- L. A. Lyustemik, On a class of nonlinear operators in Hilbert space, Izv. Akad. Nauk SSSR Ser. Mat. 3 (1939), 257-264. (Russian)
- 41.
- J. Mawhin, L, Boll. Un. Mat. Ital. 10 (1974), 343-354. MR 369823
- 42.
- J. Mawhin and M. Willem, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations (to appear). MR 741271
- 43.
- P. J. McKenna and J. Rauch, Strongly nonlinear perturbations of nonnegative boundary value problems with kernel, J. Differential Equations 29 (1978), 253-265. MR 491053
- 44.
- J. Necas, On the range of nonlinear operators with linear asymptotes which are not invertible, Comment. Math. Univ. Carolinae 14 (1973), 63-72. MR 318995
- 45.
- L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 267-302. MR 609039
- 46.
- E. Podolak, On the range of operator equations with an asymptotically nonlinear term, Indiana Univ. Math. J. 25 (1976), 1127-1137. MR 425698
- 47.
- P. H. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear Analysis: A collection of Paper in Honor of Erich H. Rothe (L. Cesari, R. Kannan, and H. F. Weinberger, eds.), Academic Press, New York, 1978, pp. 161-177. MR 501092
- 48.
- B. Ruf, On nonlinear problems with jumping nonlinearities, Ann. Mat. Pura Appl. 128 (1981), 133-151. MR 640779
- 49.
- D. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 21 (1972), 979-1000. MR 299921
- 50.
- S. Solimini, Existence of a third solution for a class of boundary value problems with jumping nonlinearities, preprint.
- 51.
- M. Struwe, Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems, Manuscripta Math. (1980), 335-364. MR 595426
Additional Information:
Reviewer(s):
Alan C.
Lazer
Review Information:
Journal:
Bull. Amer. Math. Soc.
8
(1983),
482-489.
DOI:
10.1090/S0273-0979-1983-15129-7
PII:
S 0273-0979(1983)15129-7
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