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 ($$p-1$$p-1)-linear near $$+\infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-\Delta _p,W^{1,p}_0(\Omega ))$$(-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 $$\lambda >0$$λ>0.