# Quasi-Periodic Solutions in Nonlinear Asymmetric Oscillations

### Xiaojing Yang

Tsinghua University, Beijing, China### KUEIMING LO

Tsinghua University, Beijing, China

## Abstract

The existence of Aubry–Mather sets and infinitely many subharmonic solutions to the following $p$-Laplacian like nonlinear equation

$(p−1)_{−1}(ϕ_{p}(x_{′}))_{′}+[αϕ_{p}(x_{+})−βϕ_{p}(x_{−})]+g(x)=h(t)$

is discussed, where $ϕ_{p}(u)=∣u∣_{p−2}u,p>1$, $α,β$ are positive constants satisfying $α_{−p1}+β_{−p1}=n2 $ with $n∈N$, $h$ is piece-wise two times differentiable and $2π_{p}$-periodic, $g∈C_{1}(R)$ is bounded, $x_{±}=max{±x,0}$, $π_{p}=psin(π/p)2π .$

## Cite this article

Xiaojing Yang, KUEIMING LO, Quasi-Periodic Solutions in Nonlinear Asymmetric Oscillations. Z. Anal. Anwend. 26 (2007), no. 2, pp. 207–220

DOI 10.4171/ZAA/1319