A fractional eigenvalue problem in $\mathbb{R}^N$

TL;DR

This paper proves the existence of eigenvalues for a linear fractional operator with a constant lower order term in the entire space, advancing the understanding of fractional eigenvalue problems.

Contribution

It establishes the existence of eigenvalues for a class of fractional operators in unbounded domains, which was previously unknown.

Findings

Eigenvalues exist for the considered fractional operator.

The operator's spectral properties are characterized in the whole space.

The results extend classical eigenvalue theory to fractional operators.

Abstract

We prove that a linear fractional operator with an asymptotically constant lower order term in the whole space admits eigenvalues.