A sub-supersolution method for nonlinear elliptic singular systems with natural growth and some applications. (February 2016)

• Record Type: Journal Article
• Authors: Carmona, José; Martínez-Aparicio, Pedro J.; Suárez, Antonio
• Is Part Of: Nonlinear analysis. Volume 132(2016)
• Page Start: 47
• Page End: 65
• Publication Date: 2016-02
• Subjects: 35B09 -- 35B51 -- 35D30 -- 35J60 -- 35J75 -- 92B05; Sub-supersolution method -- Singular gradient systems -- Lotka–Volterra; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.10.022
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we give a sub-supersolution method for nonlinear elliptic singular systems with quadratic gradient whose model system is the following { − Δ u + v β | ∇ u | 2 u α = f 1 ( x, u, v ) in Ω, − Δ v + u μ | ∇ v | 2 v γ = f 2 ( x, u, v ) in Ω, u = v = 0 on ∂ Ω, where Ω is a smooth bounded domain of R N ( N ≥ 3 ), β, μ ≥ 0, 0 < α, γ < 1 and regular f 1, f 2 functions. Moreover, we apply it to prove existence of solution for some systems, including the classical Lotka–Volterra models with gradient terms. Specifically, we study the competition and the symbiotic Lotka–Volterra systems.