The existence of solutions for a Schrodinger equation with jumping nonlinearities crossing the essential spectrum

Chong Li, Xinyu Li

In this paper, we establish the existence of one solution for a Schrödinger equation with jumping nonlinearities: $-\Delta u+V(x)u=f(x,u)$, $x\in {\mathbb{R}}^N$, and $u(x)\to 0$, $|x|\to…