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Abstract:

A well-known result by Lazer and Leach establishes that if g: R → R is continuous and bounded with limits at infinity and m ε2 ℕ, then the resonant periodic problem u" + m2u + g(u) = p(t), u(0)-u(2π) = u'(0)-u'(2π) = 0 admits at least one solution, provided that αm(p)2+β(p)2 < 2/π|g(+∞)-g(- ∞)|, where αm(p) and βm(p) denote the m-th Fourier coefficients of the forcing term p. In this article we prove that, as it occurs in the case m = 0, the condition on g may be relaxed. In particular, no specific behavior at infinity is assumed.

Registro:

Documento: Artículo
Título:Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
Autor:Amster, P.; De Nápoli, P.
Filiación:Departamento de Matemática, Universidad de Buenos Aires and CONICET, Ciudad Universitaria, Pabellón i, (1428) Buenos Aires, Argentina
Palabras clave:Lazer-Leach conditions; Resonant problems
Año:2011
Volumen:29
Número:3
Página de inicio:757
Página de fin:767
DOI: http://dx.doi.org/10.3934/dcds.2011.29.757
Título revista:Discrete and Continuous Dynamical Systems
Título revista abreviado:Discrete Contin. Dyn. Syst.
ISSN:10780947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v29_n3_p757_Amster

Referencias:

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Citas:

---------- APA ----------
Amster, P. & De Nápoli, P. (2011) . Non-asymptotic lazer-leach type conditions for a nonlinear oscillator. Discrete and Continuous Dynamical Systems, 29(3), 757-767.
http://dx.doi.org/10.3934/dcds.2011.29.757
---------- CHICAGO ----------
Amster, P., De Nápoli, P. "Non-asymptotic lazer-leach type conditions for a nonlinear oscillator" . Discrete and Continuous Dynamical Systems 29, no. 3 (2011) : 757-767.
http://dx.doi.org/10.3934/dcds.2011.29.757
---------- MLA ----------
Amster, P., De Nápoli, P. "Non-asymptotic lazer-leach type conditions for a nonlinear oscillator" . Discrete and Continuous Dynamical Systems, vol. 29, no. 3, 2011, pp. 757-767.
http://dx.doi.org/10.3934/dcds.2011.29.757
---------- VANCOUVER ----------
Amster, P., De Nápoli, P. Non-asymptotic lazer-leach type conditions for a nonlinear oscillator. Discrete Contin. Dyn. Syst. 2011;29(3):757-767.
http://dx.doi.org/10.3934/dcds.2011.29.757