A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application
This study derives the uniqueness of positive solutions to Brézis–Oswald-type problems involving the fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi>&...
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MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/412 |
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| author | Yun-Ho Kim In Hyoun Kim |
| author_facet | Yun-Ho Kim In Hyoun Kim |
| author_sort | Yun-Ho Kim |
| collection | DOAJ |
| description | This study derives the uniqueness of positive solutions to Brézis–Oswald-type problems involving the fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian operator and discontinuous Kirchhoff-type coefficients. The Brézis–Oswald-type result and Ricceri’s abstract global minimum principle are critical tools in identifying this uniqueness. We consider an eigenvalue problem associated with fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian problems to confirm the existence of a positive solution for our problem without the Kirchhoff coefficient. Moreover, we establish the uniqueness result of the Brézis–Oswald type by exploiting a generalization of the discrete Picone inequality. |
| format | Article |
| id | doaj-art-08a2d30e1ab24db2882d77d1892d41a8 |
| institution | Matheson Library |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-08a2d30e1ab24db2882d77d1892d41a82025-07-25T13:23:29ZengMDPI AGFractal and Fractional2504-31102025-06-019741210.3390/fractalfract9070412A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its ApplicationYun-Ho Kim0In Hyoun Kim1Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of KoreaDepartment of Mathematics, Incheon National University, Incheon 22012, Republic of KoreaThis study derives the uniqueness of positive solutions to Brézis–Oswald-type problems involving the fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian operator and discontinuous Kirchhoff-type coefficients. The Brézis–Oswald-type result and Ricceri’s abstract global minimum principle are critical tools in identifying this uniqueness. We consider an eigenvalue problem associated with fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian problems to confirm the existence of a positive solution for our problem without the Kirchhoff coefficient. Moreover, we establish the uniqueness result of the Brézis–Oswald type by exploiting a generalization of the discrete Picone inequality.https://www.mdpi.com/2504-3110/9/7/412fractional (<i>r</i>, <i>q</i>)-LaplacianKirchhoff-type functionuniquenessglobal minima |
| spellingShingle | Yun-Ho Kim In Hyoun Kim A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application Fractal and Fractional fractional (<i>r</i>, <i>q</i>)-Laplacian Kirchhoff-type function uniqueness global minima |
| title | A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application |
| title_full | A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application |
| title_fullStr | A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application |
| title_full_unstemmed | A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application |
| title_short | A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application |
| title_sort | brezis oswald type result for the fractional i r i i q i laplacian problems and its application |
| topic | fractional (<i>r</i>, <i>q</i>)-Laplacian Kirchhoff-type function uniqueness global minima |
| url | https://www.mdpi.com/2504-3110/9/7/412 |
| work_keys_str_mv | AT yunhokim abrezisoswaldtyperesultforthefractionaliriiqilaplacianproblemsanditsapplication AT inhyounkim abrezisoswaldtyperesultforthefractionaliriiqilaplacianproblemsanditsapplication AT yunhokim brezisoswaldtyperesultforthefractionaliriiqilaplacianproblemsanditsapplication AT inhyounkim brezisoswaldtyperesultforthefractionaliriiqilaplacianproblemsanditsapplication |