We consider a nonlinear elliptic Dirichlet problem driven by the (p,q)-Laplacian and a reaction consisting of a parametric singular term plus a Caratheodory perturbation f(z,x) which is (p-1)-linear as x goes to + infinity. First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter lambda>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*_lambda and investigate the monotonicity and continuity properties of the map lambda --> u*_lambda.
Papageorgiou N.S., Vetro C., & Zhang Y. (2020). Positive solutions for parametric singular Dirichlet (p,q)-equations. NONLINEAR ANALYSIS, 198, 1-23.
Data di pubblicazione: | 2020 |
Titolo: | Positive solutions for parametric singular Dirichlet (p,q)-equations |
Autori: | |
Citazione: | Papageorgiou N.S., Vetro C., & Zhang Y. (2020). Positive solutions for parametric singular Dirichlet (p,q)-equations. NONLINEAR ANALYSIS, 198, 1-23. |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.na.2020.111882 |
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 Caratheodory perturbation f(z,x) which is (p-1)-linear as x goes to + infinity. First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter lambda>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*_lambda and investigate the monotonicity and continuity properties of the map lambda --> u*_lambda. |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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