Existence of blow-up solutions for a class of elliptic system with convection term

TL;DR

This paper proves the existence of blow-up solutions for a broad class of elliptic systems with convection terms, using sub and supersolution methods that account for gradient-dependent nonlinearities.

Contribution

It introduces a new approach to establish blow-up solutions for elliptic systems with gradient-dependent nonlinearities using sub and supersolution techniques.

Findings

Established existence of blow-up solutions for systems with convection terms.

Extended sub and supersolution methods to gradient-dependent nonlinearities.

Applicable to a wide class of elliptic systems.

Abstract

The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of the gradient of the solution. This result permits to study the existence of blow-up solution for a large class of systems.