# Quasi-periodic solutions for second order differential equation with superlinear asymmetric nonlinearities and nonlinear damping term

Research paper by Xiaoming Wang

Indexed on: 18 Jun '15Published on: 18 Jun '15Published in: Boundary Value Problems

#### Abstract

In this paper, the existence of Aubry-Mather sets and quasi-periodic solutions of the oscillator $$x''+\alpha{x^{+}}^{3}-\beta{x^{-}}^{3}+f(x)q(x')+\psi(x)=p(t)$$ are established, where f, q, and ψ belong to the class $$C^{1}(R)$$, p is a continuous 2π-periodic function. Under some assumptions on the parities of f, ψ, and p, we prove that there are infinitely many generalized quasi-periodic solutions by a result of Shuinee Chow and Mingliang Pei from the Aubry-Mather theorem of reversible mappings.