Existence and uniqueness of solutions for a nonlinear equation with convection term

TL;DR

This paper establishes the existence and uniqueness of weak solutions for a nonlinear elliptic equation with variable exponent and convection term, using topological degree theory to extend previous results.

Contribution

It introduces a new approach employing topological degree theory to prove existence and uniqueness for a class of nonlinear elliptic equations with variable exponents and convection.

Findings

Proved existence of at least one weak solution under Leray-Lions and growth conditions.

Established uniqueness of solutions under additional assumptions.

Generalized and improved previous results in the field.

Abstract

In this paper, we consider the existence and uniqueness of weak solutions of a nonlinear elliptic equation with a variable exponent, a monotonic type operator and a convection term. With the topological degree theory, we prove the existence of at least one weak solution under some Leray-Lions and growth conditions. Moreover, we obtain the uniqueness of the solution of the problem under some additional assumptions. Our results generalize and improve existing results with another approach.