Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application
The aim of this paper is to establish the existence and uniqueness of solutions to non-local problems involving a discontinuous Kirchhoff-type function via a global minimum principle of Ricceri. More precisely, we first obtain the uniqueness result of weak solutions to nonlinear fractional Laplacian...
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2024-10-01
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| author | Yun-Ho Kim |
| author_facet | Yun-Ho Kim |
| author_sort | Yun-Ho Kim |
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| description | The aim of this paper is to establish the existence and uniqueness of solutions to non-local problems involving a discontinuous Kirchhoff-type function via a global minimum principle of Ricceri. More precisely, we first obtain the uniqueness result of weak solutions to nonlinear fractional Laplacian problems of Brézis–Oswald type. We then demonstrate the existence of a unique positive solution to Kirchhoff-type problems driven by the non-local fractional Laplacian as its application. The main features of the present paper are the lack of the continuity of the Kirchhoff function in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula> and the localization of a positive solution. |
| format | Article |
| id | doaj-art-d40e78c7c77944b7b7997fbe318199fd |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-d40e78c7c77944b7b7997fbe318199fd2025-08-20T02:28:05ZengMDPI AGFractal and Fractional2504-31102024-10-0181162210.3390/fractalfract8110622Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its ApplicationYun-Ho Kim0Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of KoreaThe aim of this paper is to establish the existence and uniqueness of solutions to non-local problems involving a discontinuous Kirchhoff-type function via a global minimum principle of Ricceri. More precisely, we first obtain the uniqueness result of weak solutions to nonlinear fractional Laplacian problems of Brézis–Oswald type. We then demonstrate the existence of a unique positive solution to Kirchhoff-type problems driven by the non-local fractional Laplacian as its application. The main features of the present paper are the lack of the continuity of the Kirchhoff function in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula> and the localization of a positive solution.https://www.mdpi.com/2504-3110/8/11/622fractional LaplacianKirchhoff-type functionweak solutionuniquenessglobal minima |
| spellingShingle | Yun-Ho Kim Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application Fractal and Fractional fractional Laplacian Kirchhoff-type function weak solution uniqueness global minima |
| title | Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application |
| title_full | Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application |
| title_fullStr | Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application |
| title_full_unstemmed | Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application |
| title_short | Existence and Uniqueness of Solutions to Non-Local Problems of Brézis–Oswald Type and Its Application |
| title_sort | existence and uniqueness of solutions to non local problems of brezis oswald type and its application |
| topic | fractional Laplacian Kirchhoff-type function weak solution uniqueness global minima |
| url | https://www.mdpi.com/2504-3110/8/11/622 |
| work_keys_str_mv | AT yunhokim existenceanduniquenessofsolutionstononlocalproblemsofbrezisoswaldtypeanditsapplication |