Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type
This paper is devoted to establishing multiplicity results of nontrivial weak solutions to the fractional <i>p</i>-Laplacian equations of the Kirchhoff–Schrödinger type with Hardy potentials. The main features of the paper are the appearance of the Hardy potential and nonlocal Kirchhoff...
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2024-12-01
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| author | Yun-Ho Kim |
| author_facet | Yun-Ho Kim |
| author_sort | Yun-Ho Kim |
| collection | DOAJ |
| description | This paper is devoted to establishing multiplicity results of nontrivial weak solutions to the fractional <i>p</i>-Laplacian equations of the Kirchhoff–Schrödinger type with Hardy potentials. The main features of the paper are the appearance of the Hardy potential and nonlocal Kirchhoff coefficients, and the absence of the compactness condition of the Palais–Smale type. To demonstrate the multiplicity results, we exploit the fountain theorem and the dual fountain theorem as the main tools, respectively. |
| format | Article |
| id | doaj-art-9bc776b9f7b04bb293ecd2de835d0ea1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9bc776b9f7b04bb293ecd2de835d0ea12025-01-10T13:18:04ZengMDPI AGMathematics2227-73902024-12-011314710.3390/math13010047Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy TypeYun-Ho Kim0Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of KoreaThis paper is devoted to establishing multiplicity results of nontrivial weak solutions to the fractional <i>p</i>-Laplacian equations of the Kirchhoff–Schrödinger type with Hardy potentials. The main features of the paper are the appearance of the Hardy potential and nonlocal Kirchhoff coefficients, and the absence of the compactness condition of the Palais–Smale type. To demonstrate the multiplicity results, we exploit the fountain theorem and the dual fountain theorem as the main tools, respectively.https://www.mdpi.com/2227-7390/13/1/47fractional p-LaplacianHardy potentialKirchhoff functionweak solutionvariational method |
| spellingShingle | Yun-Ho Kim Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type Mathematics fractional p-Laplacian Hardy potential Kirchhoff function weak solution variational method |
| title | Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type |
| title_full | Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type |
| title_fullStr | Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type |
| title_full_unstemmed | Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type |
| title_short | Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type |
| title_sort | multiplicity results of solutions to the fractional i p i laplacian problems of the kirchhoff schrodinger hardy type |
| topic | fractional p-Laplacian Hardy potential Kirchhoff function weak solution variational method |
| url | https://www.mdpi.com/2227-7390/13/1/47 |
| work_keys_str_mv | AT yunhokim multiplicityresultsofsolutionstothefractionalipilaplacianproblemsofthekirchhoffschrodingerhardytype |