Positive solutions for nonlinear parametric singular Dirichlet problems - Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D. (Bulletin of mathematical sciences, 2019)
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 ( − Δ p , W 0 1 , 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 .