Positive solutions for parametric (p(z),q(z))-equations

Abstract

We consider a parametric elliptic equation driven by the anisotropic (p,q)(p,q)-Laplacian. The reaction is superlinear. We prove a “bifurcation-type” theorem describing the change in the set of positive solutions as the parameter λ\lambda moves in ℝ+=(0,+∞){{\mathbb{R}}}_{+}=(0,+\infty ).

Keywords

• anisotropic regularity
• anisotropic maximum principle
• positive solutions
• minimal positive solution
• superlinear reaction
• 35j20
• 35j70