# Existence and uniqueness results for double phase problems with convection term

## TL;DR

This paper investigates quasilinear elliptic equations with double phase behavior and gradient-dependent reaction terms, establishing existence and uniqueness of weak solutions under broad conditions using pseudomonotone operator theory.

## Contribution

It provides new existence and uniqueness results for double phase problems with convection terms, expanding the understanding of such complex elliptic equations.

## Key findings

- Existence of weak solutions under general assumptions
- Uniqueness achieved with linear gradient conditions
- Application of pseudomonotone operator theory

## Abstract

In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying the theory of pseudomonotone operators. Imposing some linear conditions on the gradient variable the uniqueness of the solution is obtained.