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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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An eigenvalue problem for nonlinear elliptic partial differential equations
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by Melvyn S. Berger PDF
Trans. Amer. Math. Soc. 120 (1965), 145-184 Request permission
References
  • Shmuel Agmon, The $L_{p}$ approach to the Dirichlet problem. I. Regularity theorems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 13 (1959), 405–448. MR 125306
  • S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623–727. MR 125307, DOI 10.1002/cpa.3160120405
    • S. Banach, Über homogene polynome in ${L^2}$, Studia Math. 7 (1938), 36-44.
  • G. Bratu, Sur les Ă©quations intĂ©grales non linĂ©aires, Bull. Soc. Math. France 42 (1914), 113–142 (French). MR 1504727
  • Felix E. Browder, On the spectral theory of elliptic differential operators. I, Math. Ann. 142 (1960/61), 22–130. MR 209909, DOI 10.1007/BF01343363
  • Felix E. Browder, Functional analysis and partial differential equations. II, Math. Ann. 145 (1961/62), 81–226. MR 136857, DOI 10.1007/BF01342796
  • Felix E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862–874. MR 156116, DOI 10.1090/S0002-9904-1963-11068-X
    • —, Variational boundary value problems for quasilinear elliptic equations. I, II, III, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 31-37, 592-598, 794-798. R. Courant and D. Hilbert, Methods of mathematical physics, Vols. 1, 2, New York, 1953, 1962.
  • Ju. A. DubinskiÄ­, Some imbedding theorems in Orlicz classes, Dokl. Akad. Nauk SSSR 152 (1963), 529–532 (Russian). MR 0160109
  • G. F. D. Duff, Modified boundary value problems for a quasi-linear elliptic equation, Canadian J. Math. 8 (1956), 203–219. MR 78560, DOI 10.4153/CJM-1956-024-5
  • Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
    • L. GĂ„rding, Dirichlet’s problem for linear elliptic partial differential equations, Math. Scand. 1 (1953), 55-72.
  • David Gilbarg, Some local properties of elliptic equations, Proc. Sympos. Pure Math., Vol. IV, American Mathematical Society, Providence, R.I., 1961, pp. 127–141. MR 0133578
    • M. Golomb, Zur theorie der nichtlinearen Integralgleichungen, Math. Z. 39 (1934), 45-75. A. Granas, Introduction to the toplogy of function spaces, Lecture notes, Univ. of Chicago, Chicago, Ill., 1961.
  • A. Hammerstein, Nichtlineare Integralgleichungen nebst Anwendungen, Acta Math. 54 (1930), no. 1, 117–176 (German). MR 1555304, DOI 10.1007/BF02547519
    • G. H. Hardy, J. E. Littlewood and G. PĂłlya, Inequalities, Cambridge Univ. Press, London, 1934. A. I. Koshelev, A priori estimates in ${L_p}$ and generalized solutions of elliptic eqations and systems, Uspehi Mat. Nauk 13 (1958), 29-88; Amer. Math. Soc. Transl. (2) 20 (1962), 105-171. M. A. Krasnoselskii and Y. Rutitskii, Convex functions, Noordhoff, Groningen, 1961.
  • M. G. KreÄ­n and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk (N. S.) 3 (1948), no. 1(23), 3–95 (Russian). MR 0027128
  • O. A. LadyĆŸenskaya, Investigation of the Navier-Stokes equation for stationary motion of an incompressible fluid, Uspehi Mat. Nauk 14 (1959), no. 3, 75–97 (Russian). MR 0119676
  • Norman Levinson, Positive eigenfunctions for $\Delta u+\lambda f(u)=0$, Arch. Rational Mech. Anal. 11 (1962), 258–272. MR 145216, DOI 10.1007/BF00253940
  • J.-L. Lions, Équations diffĂ©rentielles opĂ©rationnelles et problĂšmes aux limites, Die Grundlehren der mathematischen Wissenschaften, Band 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961 (French). MR 0153974
    • L. Ljusternik, Sur une class d’équations diffĂ©rentielles non-lineaires, Mat.Sb. 44 (1937), 1143-1168. —, On a class of non-linear operators in Hilbert space, Izv. Akad. Nauk. SSSR (1939), 257-264.
  • Zeev Nehari, Characteristic values associated with a class of non-linear second-order differential equations, Acta Math. 105 (1961), 141–175. MR 123775, DOI 10.1007/BF02559588
  • Louis Nirenberg, Estimates and existence of solutions of elliptic equations, Comm. Pure Appl. Math. 9 (1956), 509–529. MR 91402, DOI 10.1002/cpa.3160090322
  • Louis Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math. 8 (1955), 649–675. MR 75415, DOI 10.1002/cpa.3160080414
  • George H. Pimbley Jr., A sublinear Sturm-Liouville problem, J. Math. Mech. 11 (1962), 121–138. MR 0138820
  • Frigyes Riesz and BĂ©la Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR 0071727
    • H. H. Schaeffer, Some non-linear eigenvalue problems, Non-Linear Problems Conference Univ. of Wisconsin, Madison, Wis., 1963.
  • Laurent Schwartz, ThĂ©orie des distributions. Tome II, Publ. Inst. Math. Univ. Strasbourg, vol. 10, Hermann & Cie, Paris, 1951 (French). MR 0041345
  • M. M. VaÄ­nberg, On the continuity of some operators of special type, Doklady Akad. Nauk SSSR (N.S.) 73 (1950), 253–255 (Russian). MR 0036451
  • M. M. VaÄ­nberg, The existence of characteristic functions for nonlinear integral equations with nonpositive kernels, Doklady Akad. Nauk SSSR (N.S.) 78 (1951), 1077–1080 (Russian). MR 0043354
    • —, Variational methods for the investigation of non-linear operators, GITTL, Moscow, 1956.
  • M. I. ViĆĄik, Boundary-value problems for quasilinear strongly elliptic systems of equations having divergence form, Dokl. Akad. Nauk SSSR 138 (1961), 518–521 (Russian). MR 0150454
  • Aurel Wintner, On the Hölder restrictions in the theory of partial differential equations, Amer. J. Math. 72 (1950), 731–738. MR 40503, DOI 10.2307/2372289
  • I. M. Gelâ€Čfand, Some problems in the theory of quasi-linear equations, Uspehi Mat. Nauk 14 (1959), no. 2 (86), 87–158 (Russian). MR 0110868
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Additional Information
  • © Copyright 1965 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 120 (1965), 145-184
  • MSC: Primary 35.47
  • DOI: https://doi.org/10.1090/S0002-9947-1965-0181821-3
  • MathSciNet review: 0181821