Unbounded solutions and periodic solutions for second order differential equations with asymmetric nonlinearity

Li, Xiong; Zhang, Ziheng

doi:10.1090/S0002-9939-07-08928-9

Unbounded solutions and periodic solutions for second order differential equations with asymmetric nonlinearity
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by Xiong Li and Ziheng Zhang PDF

Proc. Amer. Math. Soc. 135 (2007), 2769-2777 Request permission

Abstract:

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator \[ \ddot {x}+f(\dot {x})+a x^{+}-bx^{-}=\varphi (t,x), \] where $a$ and $b$ are positive constants satisfying the nonresonant condition \[ \frac {1}{\sqrt {a}}+\frac {1}{\sqrt {b}}\notin \mathbb {Q} \] and $\varphi (t,x)$ is $2\pi$-periodic in the first variable and bounded.

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