The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation

Abstract

In this paper we will construct a continuous positive periodic function $p(t)$ such that the corresponding superlinear Duffing equation $$x"+a(x)x^{2n+1}+p(t)x^{2m+1}=0,n+2\le 2m+1<2n+1$$ possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient $a(x)$ is an arbitrary positive smooth periodic function defined in the whole real axis.

References in corpus (1)

• Coexistence of bounded and unbounded motions in a bouncing ball model