Document Zbl 0375.35026

Some critical point theorems and applications to semilinear elliptic partial differential equations. (English) Zbl 0375.35026

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 5, 215-223 (1978).

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MSC:

35J60	Nonlinear elliptic equations
35A15	Variational methods applied to PDEs

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References:

[1]	A. Ambrosetti - P.H. Rabinowitz , Dual variational methods in critical point theory and applications , J. Functional Anal. , 14 ( 1973 ), pp. 349 - 381 . MR 370183 \| Zbl 0273.49063 · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[2]	P.H. Rabinowitz , Variational methods for nonlinear eigenvalue problems, Eigenvalues of Nonlinear Problems , Edizioni Cremonese , Rome ( 1974 ), pp. 141 - 195 . MR 464299
[3]	D.C. Clark , A variant of the Lusternik-Schnirelman theory , Ind. Univ. Math. J. , 22 ( 1972 ), pp. 65 - 74 . MR 296777 \| Zbl 0228.58006 · Zbl 0228.58006 · doi:10.1512/iumj.1972.22.22008
[4]	A. Dold , Lectures on Algebraic Topology , Springer-Verlag , Berlin , 1972 . MR 415602 \| Zbl 0234.55001 · Zbl 0234.55001
[5]	P.H. Rabinowitz , Free vibrations for a semitinear wave equation , to appear Comm. Pure Appl. Math. MR 470378 \| Zbl 0341.35051 · Zbl 0341.35051 · doi:10.1002/cpa.3160310203
[6]	J.T. Schwartz , Nonlinear Functional Analysis, lecture notes , Courant Inst. of Math. Sc. , New York Univ. , 1965 . MR 433481
[7]	R.S. Palais , Critical point theory and the minimax principle , Proc. Sym. Pure Math ., 15 , A.M.S . Providence, R. I. , ( 1970 ), pp. 185 - 212 . MR 264712 \| Zbl 0212.28902 · Zbl 0212.28902
[8]	P.H. Rabinowitz , Some aspects of nonlinear eigenvalue problems , Rocky Mtn. Math. J. , 3 ( 1973 ), pp. 161 - 202 . MR 320850 \| Zbl 0255.47069 · Zbl 0255.47069 · doi:10.1216/RMJ-1973-3-2-161
[9]	J. Leray - J. Schauder , Topologie et equations fonctionnelles , Ann. Sci. Ecole Norm. Sup. , 3 , 51 ( 1934 ), pp. 45 - 78 . Numdam \| MR 1509338 \| JFM 60.0322.02 · JFM 60.0322.02

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