Existence of Solutions Across Resonance in the Large for Semilinear Problems

McKenna, P.J.

McKenna, P.J.

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 64 (1978), p. 247-251 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

L’Autore considera l’equazione astratta: $Ex+\lambda x=Nx$ con $E$ operatore lineare, $N$ operatore non lineare, $\lambda$ parametro. Detti $\lambda_{0}$ e $\lambda_{1}$ due successivi autovalori di (1) (con $N=0$ ), e sotto opportune condizioni per $N$ , dimostra che esiste un $\epsilon>0$ , tale che per $\lambda_{0}—\epsilon<\lambda<\lambda_{1}$ la (1) ammette un insieme di soluzioni uniformemente limitate.

Publié le : 1978-12-01

Zbl 0446.47058

@article{RLINA_1978_8_65_6_247_0,
     author = {P.J. McKenna},
     title = {Existence of Solutions Across Resonance in the Large for Semilinear Problems},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {64},
     year = {1978},
     pages = {247-251},
     zbl = {0446.47058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1978_8_65_6_247_0}
}

McKenna, P.J. Existence of Solutions Across Resonance in the Large for Semilinear Problems. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 64 (1978) pp. 247-251. http://gdmltest.u-ga.fr/item/RLINA_1978_8_65_6_247_0/

Bibliographie

[1] Cesari, L. - (a) Teoremi di esistenza al passaggio attraverso valori critici, «Rend. Accad. Naz. Lincei». To appear, (b) An abstract existence theorem across a point of resonance, Intern. Symposium on Dynamical Systems, Gainesville, Fla., 1976. To appear, (c) Nonlinear oscillations cross a point of resonance for nonselfadjoint systems, «Journ. Diff. Equations». To appear. | MR 467420

[2] Cesari, L. - Nonlinear Analysis. A Volume in Honor of E. H. Rothe, Academic Press (to appear). | MR 499103

[3] Cesari, L. (1976) - Functional Analysis and Nonlinear Differential Equations, in a volume of the same title (Cesari, Karman, Schuur, eds.), Dekkar. | MR 487630

[4] Landesman, E.M. and Lazer, A. C. (1970) - Nonlinear perturbations of elliptic boundary value problems at resonance, «J. Math. Mech.» (19), 609-623. | MR 267269 | Zbl 0193.39203

[5] Lazer, A. C. and Leach, D. E. (1969) - Bounded perturbations of forced nonlinear oscillations at resonance, «Ann. di Mat. pura applic.», 72, 49-68. | MR 249731 | Zbl 0194.12003

[6] Mckenna, P. J. (1976) - Nonselfadjoint Semilinear Equations in the Alternative Method, Ph. D. thesis, University of Michigan.

[7] Mckenna, P. J. - Discontinuous Perturbations of Elliptic Boundary Value Problems at Resonance (to appear). | MR 502553

[8] Shaw, H. - A nonlinear elliptic boundary value problem at resonance, «Trans. Amer. Math. Soc.» (to appear). | MR 463687

[9] Shaw, H. - Nonlinear Elliptic Boundary Value Problems at Resonance, Ph. D. Thesis, University of Michigan. | Zbl 0341.35039

[10] Williams, S. (1970) - A sharp sufficient condition for solutions of a nonlinear elliptic boundary value problem, «J. Diff. Equations», 8, 580-586. | MR 267267 | Zbl 0209.13003