Critical and subcritical fractional problems with vanishing potentials

TL;DR

This paper studies fractional scalar field equations with critical and subcritical nonlinearities, focusing on cases where potentials vanish at infinity, addressing challenges related to compactness on unbounded domains.

Contribution

It introduces new methods to handle vanishing potentials in fractional problems with critical growth, expanding understanding of existence and behavior of solutions.

Findings

Established existence results for fractional problems with vanishing potentials.

Developed compactness techniques for unbounded domains with variable potentials.

Analyzed the impact of critical and subcritical nonlinearities on solution properties.

Abstract

We investigate a class of nonlinear nonautonomous scalar field equations with fractional diffusion, critical power nonlinearity and a subcritical term. The involved potentials are allowed for vanishing behavior at infinity. The problem is set on the whole space and compactness issues have to be tackled.