Quasi-Periodic Solutions in Nonlinear Asymmetric Oscillations

  • Xiaojing Yang

    Tsinghua University, Beijing, China

    Tsinghua University, Beijing, China


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

(p1)1(ϕp(x))+[\alϕp(x+)βϕp(x)]+g(x)=h(t)(p-1)^{-1}(\phi_p(x'))'+[\al\phi_p(x^+)-\beta\phi_p(x^-)]+g(x) = h(t)

is discussed, where ϕp(u)=up2u,p>1\phi_p(u)=|u|^{p-2}u, \,p>1, \,\al,β\al, \beta are \vspace{-0.05cm} positive constants satisfying \linebreak \al1p+β1p=2n\al^{-\frac{1}{p}}+\beta^{-\frac{1}{p}}=\frac2n with nN,hn\in \N, \,h is piece-wise two times differentiable and 2πp2\pi_p-periodic, gC1(R)g\in C^1(R) is bounded, x±=max{±x,0},πp=2πpsin(π/p).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