A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence. (1st December 2016)

• Record Type: Journal Article
• Authors: Motreanu, Dumitru; Vetro, Calogero; Vetro, Francesca
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 12(2016)
• Page Start: 1551
• Page End: 1561
• Publication Date: 2016-12-01
• Subjects: Dirichlet problem -- parametric problems -- (p, q)-Laplacian -- system of elliptic equations; 35J45 -- 35J55; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1219866
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the -Laplacian operators and parameters μ i ≥0 ( i = 1, 2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.