Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials

Abstract

In this study, we consider the following sublinear Schrödinger equations−Δu+Vxu=fx,u,for x∈ℝN,ux⟶0,asu⟶∞,wherefx,usatisfies some sublinear growth conditions with respect touand is not required to be integrable with respect tox. Moreover,Vis assumed to be coercive to guarantee the compactness of the embedding from working space toLpℝNfor allp∈1,2∗. We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions whenfx,uis odd inuby using the variant fountain theorem.