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 <...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10780947_v29_n3_p757_Amster |
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todo:paper_10780947_v29_n3_p757_Amster2023-10-03T16:03:38Z Non-asymptotic lazer-leach type conditions for a nonlinear oscillator Amster, P. De Nápoli, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, P. De Nápoli, P. 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. |
| format |
JOUR |
| author |
Amster, P. De Nápoli, P. |
| author_facet |
Amster, P. De Nápoli, P. |
| author_sort |
Amster, P. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_10780947_v29_n3_p757_Amster |
| work_keys_str_mv |
AT amsterp nonasymptoticlazerleachtypeconditionsforanonlinearoscillator AT denapolip nonasymptoticlazerleachtypeconditionsforanonlinearoscillator |
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