# Eigenvalue problems with unbalanced growth: Nonlinear patterns and standing wave solutions

## TL;DR

This paper investigates nonlinear eigenvalue problems with unbalanced growth, focusing on existence, non-existence, and properties of solutions using variational methods and maximum principles.

## Contribution

It introduces new results on eigenvalue problems with double-phase energy and addresses compactness issues with advanced variational techniques.

## Key findings

- Established existence of solutions under certain conditions
- Proved non-existence results in specific regimes
- Analyzed properties of solutions using maximum principles

## Abstract

We consider two classes of nonlinear eigenvalue problems with double-phase energy and lack of compactness. We establish existence and non-existence results and related properties of solutions. Our analysis combines variational methods with the generalized Pucci-Serrin maximum principle.