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(p, q)-equations with singular and concave convex nonlinearities

Papageorgiou, Nikolaos S.; Winkert, Patrick

Inst. Mathematik

We consider a nonlinear Dirichlet problem driven by the ( p ,  q )-Laplacian with 1 < q < p . The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive solutions and prove a bifurcation-type theorem describing in a precise way the set of positive solutions as the parameter varies. Moreover, we show the existence of a minimal positive solution and we study it as a function of the parameter.