What does this research mean for the field?

There exist infinitely many solutions for a specific class of fractional p-Laplacian systems involving Hardy potentials and a critical Hardy-Sobolev exponent. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to investigate the existence of solutions for a nonlocal system influenced by Hardy potentials and critical exponents.

May 30, 2026

Infinitely Many Solutions for a Nonlocal System Involving Hardy Potentials and Critical Hardy–Sobolev Exponent

Key Points

The aim is to investigate the existence of solutions for a nonlocal system influenced by Hardy potentials and critical exponents.
Applied the theory of genus
Utilized variational methods to establish solutions
Focused on fractional Laplacian systems with Hardy potentials
Proven the existence of infinitely many solutions for the system
Solutions are related to the critical Hardy–Sobolev exponent

Abstract

ABSTRACT In this work, we investigate a specific class of fractional ‐Laplacian systems with Hardy potentials and a critical Hardy–Sobolev exponent. By applying the theory of genus combined with variational methods, we establish the existence of infinitely many solutions for the given system.

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