Continuous spectrum for a double-phase unbalanced growth eigenvalue problem

TL;DR

This paper investigates an eigenvalue problem involving a double-phase differential operator with unbalanced growth, revealing that its spectrum is continuous and determined by the minimal eigenvalue of a weighted p-Laplacian.

Contribution

It introduces a novel analysis of the spectrum for a double-phase unbalanced growth eigenvalue problem using the Nehari method.

Findings

The spectrum is continuous.

The minimal eigenvalue of the weighted p-Laplacian determines the spectrum.

The Nehari method effectively analyzes the eigenvalue problem.

Abstract

We consider an eigenvalue problem for a double-phase differential operator with unbalanced growth. Using the Nehari method, we show that the problem has a continuous spectrum determined by the minimal eigenvalue of the weighted p-Laplacian.