An eigenvalue problem involving a degenerate and singular elliptic operator

TL;DR

This paper investigates an eigenvalue problem with a degenerate and singular elliptic operator on , establishing the existence of an unbounded, increasing sequence of eigenvalues, extending previous results to more general operators.

Contribution

It generalizes prior work by Szulkin and Willem to include degenerate and singular elliptic operators on the entire space.

Findings

Existence of an unbounded, increasing sequence of eigenvalues.

Extension of previous eigenvalue results to more general operators.

Framework applicable to a broader class of elliptic problems.

Abstract

We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space $\mathbb{R}^N$. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of degenerate and singular operators a result of A. Szulkin and M. Willem.