Anisotropic (p, q)-equations with gradient dependent reaction
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dusan D. Repovs · Repository of the University of Ljubljana (University of Ljubljana) · 2021
Abstract We consider a Dirichlet problem driven by the anisotropic ( p , q )-Laplacian and a reaction with gradient dependence (convection). The presence of the gradient in the source term excludes from consideration a variational approach in dealing with the qualitative analysis of this problem with unbalanced growth. Using the frozen variable method and eventually a fixed point theorem, the main result of this paper establishes that the problem has a positive smooth solution.