Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials
The aim of this paper is to demonstrate the existence of a unique positive solution to non-local fractional <i>p</i>-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 singula...
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2025-01-01
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| Series: | Mathematics |
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| author | Yun-Ho Kim |
| author_facet | Yun-Ho Kim |
| author_sort | Yun-Ho Kim |
| collection | DOAJ |
| description | The aim of this paper is to demonstrate the existence of a unique positive solution to non-local fractional <i>p</i>-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. |
| format | Article |
| id | doaj-art-b2a3e5c6289e45dfa2f7f21888941bea |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-b2a3e5c6289e45dfa2f7f21888941bea2025-01-24T13:40:08ZengMDPI AGMathematics2227-73902025-01-0113231110.3390/math13020311Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy PotentialsYun-Ho Kim0Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of KoreaThe aim of this paper is to demonstrate the existence of a unique positive solution to non-local fractional <i>p</i>-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.https://www.mdpi.com/2227-7390/13/2/311fractional <i>p</i>-LaplacianHardy potentialconcentration-compactness principlediscrete Picone inequality |
| spellingShingle | Yun-Ho Kim Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials Mathematics fractional <i>p</i>-Laplacian Hardy potential concentration-compactness principle discrete Picone inequality |
| title | Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials |
| title_full | Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials |
| title_fullStr | Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials |
| title_full_unstemmed | Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials |
| title_short | Uniqueness of Positive Solutions to Non-Local Problems of Brézis–Oswald Type Involving Hardy Potentials |
| title_sort | uniqueness of positive solutions to non local problems of brezis oswald type involving hardy potentials |
| topic | fractional <i>p</i>-Laplacian Hardy potential concentration-compactness principle discrete Picone inequality |
| url | https://www.mdpi.com/2227-7390/13/2/311 |
| work_keys_str_mv | AT yunhokim uniquenessofpositivesolutionstononlocalproblemsofbrezisoswaldtypeinvolvinghardypotentials |