On some nonlinear fractional equations involving the Bessel operator

TL;DR

This paper investigates nonlinear fractional equations involving the Bessel operator, establishing existence results under various potential function assumptions through compact embedding techniques.

Contribution

It introduces new existence results for fractional Bessel equations with variable potentials using compact embedding properties.

Findings

Existence of solutions under different potential conditions

Use of compact embedding in weighted spaces

Extension of fractional Bessel operator theory

Abstract

Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact embedding properties for weighted spaces.