Existence of infinitely many solutions for the fractional Schrödinger- Maxwell equations

Abstract

In this paper, by using variational methods and critical point theory, we shall mainly study the existence of infinitely many solutions for the following fractional Schrödinger-Maxwell equations $$(-\Delta {)}^{\alpha }u+V(x)u+\varphi u=f(x,u),in{\mathbb{R}}^3,$$ $$(-△{)}^{\alpha }\varphi =K_{\alpha }{u}^2\mathrm{in}{\mathbb{R}}^3$$ where $\alpha \in (0,1],$ $K_{\alpha }=\frac{{\pi }^{-\alpha }\Gamma (\alpha )}{{\pi }^{-(3-2\alpha )/2}\Gamma ((3-2\alpha )/2)},$ $(-\Delta {)}^{\alpha }$ stands for the fractional Laplacian. Under some more assumptions on $f,$ we get infinitely many solutions for the system.

12 pages, 0 figures

References in corpus (2)

• Fractional Quantum Mechanics
• Tunneling in Fractional Quantum Mechanics