On global instability of solutions to hyperbolic equations with non-Lipschitz nonlinearity

Abstract

In a bounded domain $\Omega \subset \mathbb{R}^n$, we consider the following hyperbolic equation \begin{equation*} \begin{cases} v_{tt} = \Delta_p v+\lambda |v|^{p-2}v-|v|^{\alpha-2}v,& x\in \Omega, \\ v\bigr{|}_{\partial \Omega}=0. \end{cases} \end{equation*} We assume that $1<\alpha