Non-asymptotic lazer-leach type conditions for a nonlinear oscillator

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 <...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Amster, Pablo Gustavo, De Napoli, Pablo Luis
Publicado: 2011
Materias:
Lazer-Leach conditions
Resonant problems
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v29_n3_p757_Amster
http://hdl.handle.net/20.500.12110/paper_10780947_v29_n3_p757_Amster
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10780947_v29_n3_p757_Amster
record_format dspace
spelling paper:paper_10780947_v29_n3_p757_Amster2023-06-08T16:05:33Z Non-asymptotic lazer-leach type conditions for a nonlinear oscillator Amster, Pablo Gustavo De Napoli, Pablo Luis Lazer-Leach conditions Resonant problems 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. Fil:Amster, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:De Nápoli, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v29_n3_p757_Amster http://hdl.handle.net/20.500.12110/paper_10780947_v29_n3_p757_Amster
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Lazer-Leach conditions
Resonant problems
spellingShingle Lazer-Leach conditions
Resonant problems
Amster, Pablo Gustavo
De Napoli, Pablo Luis
Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
topic_facet Lazer-Leach conditions
Resonant problems
description 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.
author Amster, Pablo Gustavo
De Napoli, Pablo Luis
author_facet Amster, Pablo Gustavo
De Napoli, Pablo Luis
author_sort Amster, Pablo Gustavo
title Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
title_short Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
title_full Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
title_fullStr Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
title_full_unstemmed Non-asymptotic lazer-leach type conditions for a nonlinear oscillator
title_sort non-asymptotic lazer-leach type conditions for a nonlinear oscillator
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v29_n3_p757_Amster
http://hdl.handle.net/20.500.12110/paper_10780947_v29_n3_p757_Amster
work_keys_str_mv AT amsterpablogustavo nonasymptoticlazerleachtypeconditionsforanonlinearoscillator
AT denapolipabloluis nonasymptoticlazerleachtypeconditionsforanonlinearoscillator
_version_ 1768545749374599168

Ejemplares similares