Existence Solutions for a Class of Schrödinger-Maxwell Systems with Steep Well Potential. (12th April 2022) - Yang, Guocui; Duan, Shengzhong
Abstract : In this paper, we are concerned with the system of the Schrödinger-Maxwell equations − Δ u + λ V x u + b K x ϕ u = u p − 2 u, in R 3, − Δ ϕ = K x u 2, in R 3, 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 .