Ground state solutions for Bessel fractional equations with irregular nonlinearities

TL;DR

This paper establishes the existence of ground state solutions for a class of Bessel fractional equations with irregular nonlinearities, without requiring the weight function to have a specific asymptotic profile at infinity.

Contribution

It proves the existence of solutions for fractional equations with irregular weights, extending previous results that required asymptotic conditions.

Findings

Existence of ground state solutions for the given fractional equation.

Solutions are obtained without asymptotic assumptions on the weight function.

The approach broadens the class of nonlinearities and weights for which solutions can be guaranteed.

Abstract

We consider the semilinear fractional equation $ (I-\Delta)^s u = a(x) |u|^{p-2}u$ in $\mathbb{R}^N$, where $N \geq 3$, $0<s<1$, $2<p<2N/(N-2s)$ and $a$ is a bounded weight function. Without assuming that $a$ has an asymptotic profile at infinity, we prove the existence of a ground state solution.