On the set of positive solutions for resonant Robin (p, q)-equations

Abstract

We consider a nonlinear Robin problem driven by the (p, q)-Laplacian and a parametric reaction exhibiting the competition of a concave term and of a resonant perturbation. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on ℝ̊+ = (0, +∞). Also, we determine the continuity properties of the solution multifunction.

Keywords

• nonlinear regularity
• nonlinear maximum principle
• resonance
• bifurcation-type theorem
• continuity of solution multifunction
• primary: 35j20
• secondary: 35j60