Existence of solution for a singular elliptic system with convection terms. (August 2022)

• Record Type: Journal Article
• Authors: Corrêa, Francisco Julio S.A.; dos Santos, Gelson C.G.; Tavares, Leandro S.; Muhassua, Sabado Saide
• Is Part Of: Nonlinear analysis. Volume 66(2022)
• Publication Date: 2022-08
• Subjects: Quasilinear operator -- Singular elliptic system -- Convection term -- Hardy–Sobolev inequality -- Approximation argument; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103549
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we use the dual approach introduced by Colin and Jeanjean (2004) and Liu et al. (2003) combined with a Rabinowitz's result, Galerkin's method and an approximation argument to show the existence of solution for the following quasilinear Schrödinger elliptic system with both singular and convection terms − Δ z − Δ ( z 2 ) z = μ 1 w θ 1 z − γ 1 + z α 1 + | ∇ w | η 1 in Ω, − Δ w − Δ ( w 2 ) w = μ 2 z θ 2 w − γ 2 + w α 2 + | ∇ z | η 2 in Ω, z, w > 0 in Ω, z = w = 0 on ∂ Ω, where Ω is a bounded domain of R N ( N ≥ 3 ) with smooth boundary, μ i, θ i, γ i, α i, η i > 0, i = 1, 2 are real parameters.