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

TL;DR

This paper studies the existence of solutions to a complex differential equation involving the (p,q)-Laplacian with unbounded weights and gradient-dependent convection, using abstract principles and Galerkin schemes.

Contribution

It introduces new existence results for generalized solutions to (p,q)-Laplacian systems with unbounded perturbations and gradient dependence.

Findings

Existence of generalized solutions established for the system.

Development of an abstract principle based on Galerkin scheme.

Analysis of the impact of unbounded weights on solution existence.

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 basing on the Galerkin scheme.