# Nontrivial solutions of quasilinear elliptic equations with natural growth term

## TL;DR

This paper establishes the existence of multiple solutions for a class of quasilinear elliptic equations with natural growth terms, using an adapted degree theory approach under invariant assumptions.

## Contribution

It introduces a novel adaptation of degree theory to prove multiple solutions for quasilinear elliptic equations with natural growth, invariant under diffeomorphisms.

## Key findings

- Proved existence of multiple solutions.
- Developed an adapted degree theory method.
- Applicable under invariant assumptions.

## Abstract

We prove the existence of multiple solutions for a quasilinear elliptic equation containing a term with natural growth, under assumptions that are invariant by diffeomorphism. To this purpose we develop an adaptation of degree theory.