On the existence of periodic solutions for a class of nonlinearly forced systems. Arino, O. & Chérif, A. A. Funkcial. Ekvac., 35(3):485–503, 1992. abstract bibtex This paper is concerned with the existence of $2 \pi$- periodic solutions of the perturbed Hamiltonian system $\dot x\sb 1=-p\sb 2'(x\sb 2)+ɛg(t)$, $\dot x\sb 2= p\sb 1'(x\sb 1)+ɛh(t)$, where $g(t)$ and $h(t)$ are $2 \pi$-periodic functions. It is assumed that $p\sb 1(x\sb 1)$ and $p\sb 2(x\sb 2)$ behave as polynomials as $x\sb 1$, $x\sb 2 \to 0$ and $x\sb 1$, $x\sb 2 \to \infty$. The proof uses the implicit function theorem.
@Article{ArinoCherif1992,
author = {Arino, Ovide and Ch{\'e}rif, A. A.},
title = {On the existence of periodic solutions for a class of nonlinearly forced systems},
journal = {Funkcial. Ekvac.},
year = {1992},
volume = {35},
number = {3},
pages = {485--503},
issn = {0532-8721},
abstract = {This paper is concerned with the existence of $2
\pi$- periodic solutions of the perturbed
Hamiltonian system $\dot x\sb 1=-p\sb 2'(x\sb
2)+\varepsilon g(t)$, $\dot x\sb 2= p\sb 1'(x\sb
1)+\varepsilon h(t)$, where $g(t)$ and $h(t)$ are $2
\pi$-periodic functions. It is assumed that $p\sb
1(x\sb 1)$ and $p\sb 2(x\sb 2)$ behave as
polynomials as $x\sb 1$, $x\sb 2 \to 0$ and $x\sb
1$, $x\sb 2 \to \infty$. The proof uses the implicit
function theorem.},
classmath = {*34C25 },
coden = {FESIAT},
fjournal = {Fako de l'Funkcialaj Ekvacioj Japana Matematika Societo. Funkcialaj Ekvacioj. Serio Internacia},
keywords = {periodic solutions; perturbed Hamiltonian system},
mrclass = {34C25 (34C23)},
mrnumber = {93k:34089},
mrreviewer = {Raul F. Manasevich},
reviewer = {P.Smith (Keele)},
}
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