INFINITELY MANY SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER EQUATIONS

Abstract

In this paper, we deal with the existence of infinitely many solutions for a class of sublinear Schrödinger equation $$ \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\mathbb{R}}^{N},\\ u\in H^{1}({\mathbb{R}}^{N}). \end{array} \right. $$ Under the assumptions that $\inf_{{\mathbb{R}}^{N}}V(x) \gt 0$ and $f(x, t)$ is indefinite sign and sublinear as $|t|\to +\infty$, we establish some existence criteria to guarantee that the above problem has at least one or infinitely many nontrival solutions by using the genus properties in critical point theory.