Global compactness results for nonlocal problems

TL;DR

This paper establishes a global compactness result for a class of nonlinear nonlocal problems involving the fractional p-Laplacian operator with critical growth nonlinearities, advancing understanding of solution behavior.

Contribution

It provides the first Struwe type global compactness result specifically for fractional p-Laplacian problems with critical nonlinearities.

Findings

Proves a global compactness theorem for fractional p-Laplacian problems.

Addresses challenges posed by critical growth nonlinearities.

Extends classical results to nonlocal fractional operators.

Abstract

We obtain a Struwe type global compactness result for a class of nonlinear nonlocal problems involving the fractional $p-$Laplacian operator and nonlinearities at critical growth.