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

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 → + ∞ . 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 ∗ .