Positive solutions for (p, q)-equations with convection and a sign-changing reaction

Abstract

We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction which is dependent on the gradient. We look for positive solutions and we do not assume that the reaction is nonnegative. Using a mixture of variational and topological methods (the "frozen variable" technique), we prove the existence of a positive smooth solution.

Keywords

• gradient dependent reaction
• frozen variable method
• leray-schauder alternative principle
• nonlinear regularity
• nogumo-hartman condition
• 35j60
• 35j91
• 35j92
• 35d30
• 35d35