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

Papageorgiou, NS; Vetro, C; Zhang, Y

doi:10.1016/j.na.2020.111882

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 [10.1016/j.na.2020.111882].

Data di pubblicazione:	2020
Titolo:	Positive solutions for parametric singular Dirichlet (p,q)-equations
Autori:	Papageorgiou N. S. VETRO, Calogero Zhang Y. (Corresponding) mostra contributor esterni nascondi contributor esterni
Citazione:	Papageorgiou N.S., Vetro C., & Zhang Y. (2020). Positive solutions for parametric singular Dirichlet (p,q)-equations. NONLINEAR ANALYSIS, 198, 1-23 [10.1016/j.na.2020.111882].
Rivista:	NONLINEAR ANALYSIS
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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http://hdl.handle.net/10447/425872

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