# 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

\[ (p-1)^{-1}(\phi_p(x'))'+[\al\phi_p(x^+)-\beta\phi_p(x^-)]+g(x) = h(t) \]is discussed, where $ϕ_{p}(u)=∣u∣_{p−2}u,p>1$, \,\( \al, \beta \) are \vspace{-0.05cm} positive constants satisfying \linebreak \( \al^{-\frac{1}{p}}+\beta^{-\frac{1}{p}}=\frac2n \) 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