Existence and Multiplicity of Solutions for Sublinear Schr?dinger Equations with Coercive Potentials

摘要

In this study, we consider the following sublinear Schr?dinger equations ?Δu+Vxu=fx,u,for?x∈?N,ux?0,asu?∞, where fx,u satisfies some sublinear growth conditions with respect to u and is not required to be integrable with respect to x. Moreover, V is assumed to be coercive to guarantee the compactness of the embedding from working space to Lp?N for all p∈1,2?. We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions when fx,u is odd in u by using the variant fountain theorem.