Existence of solution for a singular elliptic system with convection terms. (August 2022) - Corrêa, Francisco Julio S.A.
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.