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].

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

Vetro C.;
2020-01-01

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 MAT/05 - Analisi Matematica
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/425872
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