Positive solutions for nonlinear parametric singular Dirichlet problems

Abstract

We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is (p − 1)-linear near + ∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of (−Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter λ > 0.

Keywords

• parametric singular term
• (p − 1)-linear perturbation
• uniform nonresonance
• nonlinear regularity theory
• truncation
• strong comparison principle
• bifurcation-type theorem