Ground state solutions for the nonlinear Schrödinger-Bopp-Podolsky systems with nonperiodic potentials

Abstract

In this article we study the existence of ground-state solutions for the Schrodinger-Bopp-Podolsky  equations $$\displaylines{-\Delta u+V(x) u+\phi u  =f(x,u)  \quad\text{in } \mathbb{R}^3\cr-\Delta \phi+a^2\Delta^2\phi =4\pi u^2  \quad\text{in } \mathbb{R}^3,}$$ where \(V\in C(\mathbb{R}^3,\mathbb{R})\) has different forms on the half spaces, i.e. \(V(x)=V_1(x)\) for \(x_1>0\), and \(V(x)=V_2(x)\) for \(x_1<0\), where \(V_1,V_2\in C(\mathbb R^3)\) are periodic in each coordinate. The nonlinearity \(f\) is superlinear at infinity with subcritical   or critical growth. For more information see https://ejde.math.txstate.edu/Volumes/2024/43/abstr.html