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 $$( -Δ)^α u+V(x)u+φu=f(x,u), \hbox{in } \mathbb{R}^3 ,$$ $$ (-\triangle)^αφ=K_α u^2 \ \ \mathrm{in}\ \ \mathbb{R}^3 $$ where $α\in (0,1],$ $K_α=\dfrac{π^{-α}Γ(α)}{π^{-(3-2α)/2}Γ((3-2α)/2)},$ $( -Δ)^α$ stands for the fractional Laplacian. Under some more assumptions on $f,$ we get infinitely many solutions for the system.

Theorems & Definitions (10)

• Remark 1.1
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• proof : Proof of Theorem \ref{['FSMeq thm1.1']}.