Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials

Yun-Ho Kim ()
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Yun-Ho Kim: Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea

Mathematics, 2025, vol. 13, issue 2, 1-18

Abstract: The aim of this paper is to demonstrate the existence of a unique positive solution to non-local fractional p -Laplacian equations of the Brézis–Oswald type involving Hardy potentials. The main feature of this paper is solving the difficulty that arises in the presence of a singular coefficient and in the lack of the semicontinuity property of an energy functional associated with the relevant problem. The main tool for overcoming this difficulty is the concentration–compactness principle in fractional Sobolev spaces. Also, the uniqueness result of the Brézis–Oswald type is obtained by exploiting the discrete Picone inequality.

Keywords: fractional p -Laplacian; Hardy potential; concentration-compactness principle; discrete Picone inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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