Upper bound for the number of eigenvalues for nonlinear operators

Fučik, S.; Nečas, J.; Souček, J.; Souček, V.

Fučik, S. ; Nečas, J. ; Souček, J. ; Souček, V.

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 27 (1973) no. 1, p. 53-71

MR 372918 | Zbl 0263.58007

@article{ASNSP_1973_3_27_1_53_0,
     author = {Fu\v cik, S. and Ne\v cas, Jind\v rich and Sou\v cek, J. and Sou\v cek, V.},
     title = {Upper bound for the number of eigenvalues for nonlinear operators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 27},
     number = {1},
     year = {1973},
     pages = {53-71},
     zbl = {0263.58007},
     mrnumber = {372918},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1973_3_27_1_53_0}
}

Fučik, S.; Nečas, J.; Souček, J.; Souček, V. Upper bound for the number of eigenvalues for nonlinear operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 27 (1973) no. 1, pp. 53-71. http://www.numdam.org/item/ASNSP_1973_3_27_1_53_0/

Bibliographie

[1] A. Alicxiewicz, W. Orlicz: Analytic operation8 in real Banaoh apaces, Studia Math. XIV, 1954, 57-78. | Zbl 0052.34601

[2] M.S. Berger: An eigenvalue problem for nonlinear elliptic partial differential equations, Trans. Amer. Math. Soc., 120, 1965, 145-184. | MR 181821 | Zbl 0142.08402

[3] F.E. Browder: Infinite dimensional ananifolds and nonlinear elliptic eigenvalue problems, Annals of Math. 82, 1965, 459-477. | MR 203249 | Zbl 0136.12002

[4] E.S. Citlanadze: Bxistence theorearas for minimax points in Banach apaces (in Russian) Trudy Mosk. Mat. Obšč. 2, 1953, 235-274. | MR 55574

[5] S Fu6Ik: Fredholnt alternative for nonlinear operators in Banach spaces and its applications to the differeaatial and integral equations, Cas. pro pest. mat. 1971, No. 4.

[6] S Fučík: Note on the Fredholm alternative for nonlinear operators, Comment. Math. Univ. Carolinae 12, 1971, 213-226. | MR 288641 | Zbl 0215.21201

[7] S. Fučík - J. Nečas: Ljusternik-,Sch,nirelmann theorem and nonlinear eigenvalue probletit8, Math. Nachr. 53, 1972, 277-289 | MR 333863 | Zbl 0215.21202

[8] E. H-R.S. Philips: Functional analysis and semigroups, Providence 1957. | Zbl 0078.10004

[9] M.A. Krasnoselskij: Topological methods in the theory of nonlinear integral equations, Pergamon Press, N. Y. 1964. | Zbl 0111.30303

[10] M. Kučera: Fredholm alternative for nonlinear operators, Comment. Math. Univ. Carolinae 11, 1970, 337-363. | MR 267429 | Zbl 0198.18602

[11] L.A. Ljusternik: On a class of nonlinear operators in Hilbert space (in Russian) Izv. Ak. Nank SSSR, ser. mat., No 5, 1939, 257-264.

[12] L.A. Ljusternik - L.G. Schnirelmann: Application of topology to variationat problems (in Russian) Trudy 2. Vsesujuz, mat. sjezda 1, 1935, 224-237. | Zbl 0015.21403

[13] L.A. Ljusternik - L.G. Schnirelmann : Topological methods in variational problems and their application to the differential geometry of surface (in Russian) Uspechi Mat. Nank II, 1947, 166-217.

[14] J. Nečas: Les methodes direcfes en thérie des équations elliptiques, Academia, Praha 1967.

[15] J. Nečas: Sur l'alternative de Fredholm pour les operateurs non lineairee avec applications aux problèmes aux limites, Ann. Scuola Norm. Sup. Pisa, XXIII, 1969, 331-345. | Numdam | MR 267430 | Zbl 0187.08103

[16] J. Souček - V. Souček: The Morse-Bard theorem for real-analytic functions, Comment. Math. Univ. Carolinae, 13, 1972, 45-51. | MR 308345 | Zbl 0235.26012

[17] M.M. Vajnberg: Variational methods for the study of nonlinear operators, Holden-Day, 1964. | Zbl 0122.35501

[18] J. Nečas: On the discreteneas of the spectrum of nonlinear Sturm-Liouville equation (in Russian) Dokl. Akad. Nank SSSR, 201, 1971, 1045-1048. | MR 291547 | Zbl 0252.47071

[19] A. Kratochvíl - J. Nečas: On the dieoreteness of the speotrum of nonlinear Sturm-Liouville equation of the fourth order (in Russian) Comment. Math. Univ. Carolinae, 12, 1971, 639-653. | MR 291882 | Zbl 0229.34015

[20] J. Nečas: Fredholm alternative for nonlinear operators and applicationa to partial differeittial equations and integral equations (to appear). | Zbl 0234.47050

[21] J. Nečas: Remark on the Fredholm alternative for nonlinear operators with applioation to sntegrat equations of generalized Hammerstein type (to appear).