Positive and nodal solutions for parametric superlinear weighted [formula omitted]-equations

Abstract

We consider a nonlinear eigenvalue problem for equations driven by a weighted (p,q)-Laplacian and a superlinear reaction. We prove a global (with respect to the parameter λ>0) existence and multiplicity result. We also generate nodal (sign-changing) solutions. Finally, we determine the topological properties of the solution set and prove the continuity properties of the solution multifunction.