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Variational methods for nonlinear elliptic eigenvalue problems. (English) Zbl 0135.15802

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[1] M. Berger, A nonlinear elliptic eigenvalue problem, Dissertation, Yale University, New Haven, Conn., May 1964.
[2] Felix E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862 – 874. · Zbl 0127.31901
[3] Felix E. Browder, Nonlinear elliptic problems. II, Bull. Amer. Math. Soc. 70 (1964), 299 – 302. · Zbl 0127.31902
[4] Felix E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862 – 874. · Zbl 0127.31901
[5] Felix E. Browder, Existence and uniqueness theorems for solutions of nonlinear boundary value problems, Proc. Sympos. Appl. Math., Vol. XVII, Amer. Math. Soc., Providence, R.I., 1965, pp. 24 – 49.
[6] M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, Translated by A. H. Armstrong; translation edited by J. Burlak. A Pergamon Press Book, The Macmillan Co., New York, 1964.
[7] Norman Levinson, Positive eigenfunctions for \Delta \?+\?\?(\?)=0, Arch. Rational Mech. Anal. 11 (1962), 258 – 272. · Zbl 0108.28902 · doi:10.1007/BF00253940 · doi.org
[8] George J. Minty, on a ”monotonicity” method for the solution of non-linear equations in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1038 – 1041. · Zbl 0124.07303
[9] George J. Minty, On the monotonicity of the gradient of a convex function, Pacific J. Math. 14 (1964), 243 – 247. George J. Minty, On the solvability of nonlinear functional equations of ’monotonic’ type, Pacific J. Math. 14 (1964), 249 – 255. · Zbl 0123.10601
[10] Charles B. Morrey Jr., Multiple integral problems in the calculus of variations and related topics, Ann. Scuola Norm. Sup. Pisa (3) 14 (1960), 1 – 61. · Zbl 0094.08104
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[13] S. Smale, Morse theory and a nonlinear generalization of the Dirichlet problem, Ann. of Math. (to appear). · Zbl 0131.32305
[14] M. M. Vaĭnberg, Variational methods for investigation of nonlinear operators, GITTL, Moscow, 1956 (English transl., Holden Day Co., 1964). · Zbl 0073.10303
[15] M. M. Vaĭnberg and R. I. Kačurovskiĭ, On the variational theory of non-linear operators and equations, Dokl. Akad. Nauk SSSR 129 (1959), 1199 – 1202 (Russian). · Zbl 0094.10801
[16] M. I. Višik, Quasi-linear strongly elliptic systems of differential equations of divergence form, Trudy Moskov. Mat. Obšč. 12 (1963), 125 – 184 (Russian).
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