Amann, Herbert A note on degree theory for gradient mappings. (English) Zbl 0501.58012 Proc. Am. Math. Soc. 85, 591-595 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 54 Documents MSC: 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 47H10 Fixed-point theorems 34G20 Nonlinear differential equations in abstract spaces Keywords:functional on a Hilbert space; Leray-Schauder degree; nonlinear Dirichlet problem Citations:Zbl 0307.47058 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Alfonso Castro and A. C. Lazer, Critical point theory and the number of solutions of a nonlinear Dirichlet problem, Ann. Mat. Pura Appl. (4) 120 (1979), 113 – 137. · Zbl 0426.35038 · doi:10.1007/BF02411940 [2] Kung Ching Chang, Solutions of asymptotically linear operator equations via Morse theory, Comm. Pure Appl. Math. 34 (1981), no. 5, 693 – 712. · Zbl 0444.58008 · doi:10.1002/cpa.3160340503 [3] Klaus Deimling, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, Vol. 596, Springer-Verlag, Berlin-New York, 1977. · Zbl 0361.34050 [4] M. A. Krasnosel\(^{\prime}\)skiĭ, The operator of translation along the trajectories of differential equations, Translations of Mathematical Monographs, Vol. 19. Translated from the Russian by Scripta Technica, American Mathematical Society, Providence, R.I., 1968. [5] Robert H. Martin Jr., Nonlinear operators and differential equations in Banach spaces, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1976. Pure and Applied Mathematics. [6] L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 3, 267 – 302. · Zbl 0468.47040 [7] Paul H. Rabinowitz, A note on topological degree for potential operators, J. Math. Anal. Appl. 51 (1975), no. 2, 483 – 492. · Zbl 0307.47058 · doi:10.1016/0022-247X(75)90134-1 [8] Erich H. Rothe, A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors, Math. Nachr. 4 (1951), 12 – 17. · Zbl 0044.31903 · doi:10.1002/mana.19500040103 [9] K. Thews, Untere Schranken für die Anzahl von Lösungen einer Klasse nichtlinearer Dirichlet-probleme, Doctoral Dissertation, Bochum, 1978. [10] M. M. Vainberg, Variational methods for the study of nonlinear operators, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1964. With a chapter on Newton’s method by L. V. Kantorovich and G. P. Akilov. Translated and supplemented by Amiel Feinstein. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.