Existence of positive solutions for nonlinear elliptic equations with convection terms. (March 2017)

• Record Type: Journal Article
• Authors: Motreanu, D.; Tanaka, M.
• Is Part Of: Nonlinear analysis. Volume 152(2017)
• Page Start: 38
• Page End: 60
• Publication Date: 2017-03
• Subjects: Nonlinear elliptic equation -- Convection term -- Strong maximum principle; 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.2016.12.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove the existence of positive solutions for the equation − ∑ i = 1 N ∂ ∂ x i a i ( x, u, ∇ u ) = f ( x, u, ∇ u ) in Ω under the Dirichlet boundary condition, where the essential point is the dependence of the terms of the elliptic equation on the solution u and its gradient ∇ u . We develop an approach based on approximate solutions and on a new strong maximum principle.