Periodicsolutions of Liénard equations with resonant isochronouspotentials

Tiantian Ma; Zaihong Wang

doi:10.3934/dcds.2013.33.1563

Article Contents

2013, Volume 33, Issue 4: 1563-1581. Doi: 10.3934/dcds.2013.33.1563

This issue Previous Article SRB attractors with intermingled basins for non-hyperbolic diffeomorphisms Next Article Boundary stabilization of the waves in partially rectangular domains

Periodic solutions of Liénard equations with resonant isochronous potentials

Tiantian Ma^1, and
Zaihong Wang^1,

1.
School of Mathematical Sciences, Capital Normal University, Beijing 100048

Received: August 31, 2011

Revised: August 31, 2012

Published: March 2013

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Abstract

In this paper, we study the existence and multiplicity of periodic solutions of Liénard equations $$ x''+f(x)x'+V'(x)+g(x)=p(t), $$ where $V$ is a $2\pi/n$-isochronous potential. When $F(F(x)=\int_0^xf(s)ds)$ and $g$ are bounded, we provide new sufficient conditions to ensure the existence of periodic solutions of this equations. Moreover, we prove the multiplicity of periodic solutions of the given equations under certain bounded conditions by using topological degree method. When $F, g$ satisfy a certain class of unbounded conditions, we also give sufficient conditions to ensure the existence of $2\pi$-periodic solutions of the given equations.

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Mathematics Subject Classification: Primary: 34C25; Secondary: 34B15.

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