Positive solutions for parametric singular Dirichlet (p, q)-equations. (September 2020)

• Record Type: Journal Article
• Authors: Papageorgiou, Nikolaos S.; Vetro, Calogero; Zhang, Youpei
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35J20 -- 35J75 -- 35J92; Nonlinear regularity -- Nonlinear maximum principle -- Bifurcation-type theorem -- Solution multifunction -- Minimal solution; 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.2020.111882
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a nonlinear elliptic Dirichlet problem driven by the ( p, q ) -Laplacian and a reaction consisting of a parametric singular term plus a Carathéodory perturbation f ( z, x ) which is ( p − 1 ) -linear as x → + ∞ . First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter λ > 0 moves. Subsequently, we focus on the solution multifunction and prove its continuity properties. Finally we prove the existence of a smallest (minimal) solution u λ ∗ and investigate the monotonicity and continuity properties of the map λ → u λ ∗ .