Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 43, pp. 1-25.

Title: Ground state solutions for nonlinear Schr\"odinger-Bopp-Podolsky systems with nonperiodic potentials

Authors: Qiaoyun Jiang (Chongqing Technology and Business Univ., Chongqing, China)
         Lin Li (Chongqing Technology and Business Univ., Chongqing, China)
         Shangjie Chen (Chongqing Technology and Business Univ., Chongqing, China)
         Gaetano Siciliano (Univ. degli Studi di Bari, Italy)

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.

Submitted April 22, 2024. Published August 12, 2024.
Math Subject Classifications: 35B38, 35A15, 35Q55.
Key Words:  Schrodinger-Bopp-Podolsky equation; variational method;  Nehari manifold; critical growth.