Existence Solutions for a Class of Schrödinger-Maxwell Systems with Steep Well Potential - Guocui Yang; Shengzhong Duan (Journal of Function Spaces)
In this paper, we are concerned with the system of the Schrödinger-Maxwell equations −Δu+λVxu+bKxϕu=up−2u,in R3,−Δϕ=Kxu2,in R3, where λ,b>0 are constants, and 3<p<6. Under appropriate assumptions on V and K, we prove the existence of positive solutions in the case 3<p<4 via the truncation technique. Moreover, suppose that V may change sign, we also obtain the multiplicity of solutions for the case 4<p<6.