Multiple solutions for Schrodinger-Maxwell systems with unbounded and decaying radial potentials

Abstract

This article concerns the nonlinear Schrodinger-Maxwell system $$\displaylines{ -\Delta u +V(|x|)u +Q(|x|)\phi u=Q(|x|) f(u),\quad \hbox{in } \mathbb{R}^3\cr -\Delta \phi =Q(|x|) u^{2}, \quad \hbox{in } \mathbb{R}^3 }$$ where V and Q are unbounded and decaying radial. Under suitable assumptions on nonlinearity f(u), we establish the existence of nontrivial solutions and a sequence of high energy solutions in weighted Sobolev space via Mountain Pass Theorem and symmetric Mountain Pass Theorem.

Keywords

• Schrodinger-Maxwell system
• unbounded or decaying potential
• weighted Sobolev space
• mountain pass theorem