# 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 $\phi_p(u)=|u|^{p-2}u, \,p>1$, \,$\al, \beta$ are \vspace{-0.05cm} positive constants satisfying \linebreak $\al^{-\frac{1}{p}}+\beta^{-\frac{1}{p}}=\frac2n$ with $n\in \N, \,h$ is piece-wise two times differentiable and $2\pi_p$-periodic, $g\in C^1(R)$ is bounded, $x^{\pm}=\max \{\pm x, 0\}, \,\pi_p=\frac{2\pi}{p\sin(\pi/p)}.$

## 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