A Note on Existence of a Bound State for a Non-Autonomous Nonlinear Scalar Field Equation

Abstract

The aim of this paper is to present a positive solution of a semilinear elliptic equation in $\mathbb{R}^{N}$ with non-autonomous non-linearities which are not necessarily pure-powers, nor homogeneous, and which are superlinear or asymptotically linear at infinity. The proof is variational combined with topological arguments.