Existence Solutions for a Class of Schrödinger-Maxwell Systems with Steep Well Potential. (12th April 2022)

• Record Type: Journal Article
• Authors: Yang, Guocui; Duan, Shengzhong
• Other Names: Mophou Gisele Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-04-12
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/6791308
• Languages: English
• ISSNs: 2314-8896

Abstract

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 .