A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods
Abstract In the present paper, we are concerned with the existence of nonnegative solutions for two Kirchhoff-type problems driven by a fractional p-Laplacian operator, ( − Δ ) p s $(-\Delta )_{p}^{s}$ , in a bounded smooth domain Ω of R N $\mathbb{R}^{N}$ with N > p s $N>ps$ . by employing ap...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-024-01981-w |
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| author | Omar Djidel Kheireddine Biroud Med-Salem Rezaoui Salah Boulaaras Rafik Guefaifia |
| author_facet | Omar Djidel Kheireddine Biroud Med-Salem Rezaoui Salah Boulaaras Rafik Guefaifia |
| author_sort | Omar Djidel |
| collection | DOAJ |
| description | Abstract In the present paper, we are concerned with the existence of nonnegative solutions for two Kirchhoff-type problems driven by a fractional p-Laplacian operator, ( − Δ ) p s $(-\Delta )_{p}^{s}$ , in a bounded smooth domain Ω of R N $\mathbb{R}^{N}$ with N > p s $N>ps$ . by employing approximation methods, we establish the existence of nonnegative solutions for each problems under some hypotheses on f , g : Ω × R → R $f,g : \Omega \times \mathbb{R}\to \mathbb{R}$ and weak conditions on the diffusion coefficients M , N : ( 0 , + ∞ ) → R $\mathcal{M}, \mathcal{N} :(0,+\infty )\to \mathbb{R}$ that we will present. The regularity of finite-energy solutions of both problems is also studied by imposing a few extra hypotheses on Ω, f, and g. |
| format | Article |
| id | doaj-art-eb01bd409bd744e28c4ec5ec70822b95 |
| institution | OA Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-eb01bd409bd744e28c4ec5ec70822b952025-08-20T01:57:16ZengSpringerOpenBoundary Value Problems1687-27702024-12-012024112010.1186/s13661-024-01981-wA study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methodsOmar Djidel0Kheireddine Biroud1Med-Salem Rezaoui2Salah Boulaaras3Rafik Guefaifia4Laboratory of Algebra and Number Theory (ATN) Algeria, Faculty of Mathematics, University of Algiers (USTHB)Laboratoire d’Analyse Nonlinéaire et Mathématiques Appliquées, Ecole Supŕieure de Management de TlemcenLaboratory of Algebra and Number Theory (ATN) Algeria, Faculty of Mathematics, University of Algiers (USTHB)Department of Mathematics, College of Sciences, Qassim UniversityDepartment of Mathematics, College of Sciences, Qassim UniversityAbstract In the present paper, we are concerned with the existence of nonnegative solutions for two Kirchhoff-type problems driven by a fractional p-Laplacian operator, ( − Δ ) p s $(-\Delta )_{p}^{s}$ , in a bounded smooth domain Ω of R N $\mathbb{R}^{N}$ with N > p s $N>ps$ . by employing approximation methods, we establish the existence of nonnegative solutions for each problems under some hypotheses on f , g : Ω × R → R $f,g : \Omega \times \mathbb{R}\to \mathbb{R}$ and weak conditions on the diffusion coefficients M , N : ( 0 , + ∞ ) → R $\mathcal{M}, \mathcal{N} :(0,+\infty )\to \mathbb{R}$ that we will present. The regularity of finite-energy solutions of both problems is also studied by imposing a few extra hypotheses on Ω, f, and g.https://doi.org/10.1186/s13661-024-01981-wStationary Kirchhoff problemsNonlocal p-Laplacian operatorNontrivial solutionPositive solutionApproximation methodRegularity |
| spellingShingle | Omar Djidel Kheireddine Biroud Med-Salem Rezaoui Salah Boulaaras Rafik Guefaifia A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods Boundary Value Problems Stationary Kirchhoff problems Nonlocal p-Laplacian operator Nontrivial solution Positive solution Approximation method Regularity |
| title | A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods |
| title_full | A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods |
| title_fullStr | A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods |
| title_full_unstemmed | A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods |
| title_short | A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods |
| title_sort | study of the nonlocal solution of p laplacian fractional elliptic problems via approximation methods |
| topic | Stationary Kirchhoff problems Nonlocal p-Laplacian operator Nontrivial solution Positive solution Approximation method Regularity |
| url | https://doi.org/10.1186/s13661-024-01981-w |
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