New super-quadratic conditions for asymptotically periodic Schrödinger equation
Xianhua Tang · arXiv (Cornell University) · 2015
This paper is dedicated to studying the semilinear Schrödinger equation $\left\{\begin{array}{ll}-\Nabla u+V(x)u=f(x, u), \ \ \ \ x\in {\R}^{N},u\in H^{1}({\R}^{N}),\end{array}\right.$ where $f$ is a superlinear, subcritical nonlinearity. It focuses on the case where $V(x)=V_0(x)+V_1(x)$, $V_0\in C(\R^N)$, $V_0(x)$ is 1-periodic in each of $x_1, x_2, \ldots, x_N$ and $\sup[σ(-\triangle +V_0)\cap (-\infty, 0)]<0