Local multiplicity for fractional linear equations with Hardy potentials

TL;DR

This paper demonstrates the existence of non-trivial, radial solutions to fractional linear Schrödinger equations with Hardy potentials, highlighting differences from local cases.

Contribution

It establishes the existence of solutions for fractional Schrödinger equations with Hardy potentials, contrasting with known results in local equations.

Findings

Existence of non-trivial radial solutions.

Solutions vanish at the origin.

Results differ from local Schrödinger equations.

Abstract

We exhibit existence of non-trivial solutions of some fractional linear Schr\"odinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the presence of a Hardy potential.