bdim: Biblioteca Digitale Italiana di Matematica

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Referenza completa

Cesari, Lamberto:
Teoremi di esistenza al passaggio attraverso valori critici
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 60 (1976), fasc. n.3, p. 198-201, (Italian)
pdf (437 Kb), djvu (564 Kb). | MR 0493556 | Zbl 0364.47029

Sunto

Under sole qualitative hypotheses in the large the author has proved the existence of equibounded solutions to nonlinear operational equations in a Hilbert space when a parameter describes an interval containing a point of resonance. Applications have been made to problems of periodic solutions, and to elliptic problems.
Referenze Bibliografiche
[1] L. CESARI (1963) — Functional analysis and periodic solutions of nonlinear differential equations, «Contributions to Differential Equations», 1, 149-187, Wiley. | MR 151678
[2] L. CESARI (1975) - Alternative methods in nonlinear analysis. International Conference on Differential Equations, Los Angeles. Acad. Press (Antosiewicz ed.), 95-148. | Zbl 0316.47039
[3] L. CESARI (1976) - Functional analysis, nonlinear differential equations, and the alternative method. (Un corso di lezioni al «Summer Institute» alla Michigan State University, East Lansing, Michigan, Giugno 1975). Functional Analysis and Nonlinear Differential Equations. Academic Press (Cesari, Kannar, Schuur eds.), 1976. | MR 477808
[4] L. CESARI e R. KANNAN (1976) — An abstract existence theorem at resonance, «Proc. Amer. Math. Soc.». In corso di stampa. | fulltext (doi) | MR 448180
[5] DE FIGUEIREDO (1975) - The Dirichlet problem for nonlinear elliptic equations: a Hilbert space approach. Partial Differential Equations and Related Topics. (Dold and Eckman ed.) Springer Verlag, «Lecture Notes Math.», 446, 144-165. | MR 437924
[6] R. KANNAN e P. J. MCKENNA - Problems at resonance in an abstract formulation, «Boll. Un. Mat. Italiana». In corso di stampa.
[7] E. M. LANDESMAN e A. C. LAZER (1970) - Nonlinear perturbations of linear elliptic boundary balue problems at resonance, «Journ. Math. Mech.», 19, 609-623. | MR 267269 | Zbl 0193.39203
[8] A. C. LAZER e D. E. LEACH (1969) — Bounded perturbations of forced harmonic oscillations at resonance, «Annali di Matematica Pura e Appl.», 72, 49-68. | fulltext (doi) | MR 249731 | Zbl 0194.12003
[9] J. NECAS (1973) - On the range of nonlinear operators with linear asymptotes which are not invertible, «Comm. Math. Univ. Caroliniensis», 14, 63-72. | fulltext EuDML | MR 318995 | Zbl 0257.47032
[10] H. SHAW (1976) - A nonlinear elliptic boundary value problem at resonance, «Journ. Diff. Equations». In corso di stampa | fulltext (doi) | MR 463687
[11] S. A. WILLIAMS (1970) - A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, «Journ. Diff. Equations», 8, 580-586. | fulltext (doi) | MR 267267 | Zbl 0209.13003

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