# Some recent results on the Dirichlet problem for (p,q)-Laplace equations

## TL;DR

This paper reviews recent advances in solving the Dirichlet problem for (p,q)-Laplace equations, focusing on existence, multiplicity, and various types of perturbations in bounded domains.

## Contribution

It provides a concise overview of recent theorems on existence and multiplicity for (p,q)-Laplace equations, including eigenvalue problems and perturbation effects.

## Key findings

- Existence and multiplicity theorems for (p,q)-Laplace equations
- Analysis of eigenvalue problems and perturbations
- Discussion of coercive, resonant, and critical cases

## Abstract

A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with $(p,q)$-Laplacian in a bounded domain is performed. Both eigenvalue problems and different types of perturbation terms are briefly discussed. Special attention is paid to possibly coercive, resonant, subcritical, critical, or asymmetric right-hand sides.