On competing $(p,q)$-Laplacian Dirichlet problem with unbounded weight

Abstract

We investigate the existence of generalized solutions to coercive competing system driven by the $(p, q)$-Laplacian with unbounded perturbation corresponding to the leading term in the differential operator and with convection depending on the gradient. Some abstract principle leading to the existence of generalized solutions is also derived based on the Galerkin scheme.