Positive solutions for parametric singular Dirichlet (p, q)-equations. (September 2020) - Papageorgiou, Nikolaos S.; Vetro, Calogero; Zhang, Youpei
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 Carathéodory perturbation f ( z, x ) which is ( p − 1 ) -linear as x → + ∞ . First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter λ > 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 λ ∗ and investigate the monotonicity and continuity properties of the map λ → u λ ∗ .