Positive Solutions for Resonant (p, q)-equations with convection

Abstract

We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.

Keywords

• singular term
• resonance
• nonlinear regularity
• leray-schauder alternative principle
• minimal solution
• iterative asymptotic process
• 35j60
• 35j91
• 35j92
• 35d30
• 35d35