Electron. J. Differential Equations, Vol. 2024 (2024), No. 43, pp. 1-25.
Ground state solutions for nonlinear Schr\"odinger-Bopp-Podolsky systems with nonperiodic potentials
Qiaoyun Jiang, Lin Li, Shangjie Chen, Gaetano Siciliano
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.
DOI: 10.58997/ejde.2024.43
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Qiaoyun Jiang
School of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: 1809933030@qq.com
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Lin Li
School of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: lilin420@gmail.com
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Shangjie Chen
School of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: 11183356@qq.com
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Gaetano Siciliano
Dipartimento di Matematica, Univeristà degli Studi di Bari
via E. Orabona 4, 70215 Bari, Italy
email: gaetano.siciliano@uniba.it
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