Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term - Eylem Öztürk; Nikolaos Papageorgiou (Electronic Journal of Qualitative Theory of Differential Equations)
We consider a nonlinear Robin problem driven by the anisotropic $(p,q)$-Laplacian plus an indefinite potential term. In the reaction, we have the competing effects of a parametric concave (sublinear) term perturbed by a superlinear one (concave-convex problem). We prove the existence and multiplicity result for positive solutions which is global with respect to the parameter. We also show the existence of a minimal positive solution and determine its dependence on the parameter.