Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials
This paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem. Furthermore, we discuss the fundamental properties of the representation of the solution by co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/10/568 |
| _version_ | 1797473227813945344 |
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| author | Jiabin Zuo Zakaria El Allali Said Taarabti |
| author_facet | Jiabin Zuo Zakaria El Allali Said Taarabti |
| author_sort | Jiabin Zuo |
| collection | DOAJ |
| description | This paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem. Furthermore, we discuss the fundamental properties of the representation of the solution by considering two cases. Our results not only make previous results more general but also show new insights into fourth-order elliptic problems. |
| first_indexed | 2024-03-09T20:11:53Z |
| format | Article |
| id | doaj.art-ab4bfce28edd49cbb709ec6bf1f4236c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T20:11:53Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-ab4bfce28edd49cbb709ec6bf1f4236c2023-11-24T00:11:47ZengMDPI AGFractal and Fractional2504-31102022-10-0161056810.3390/fractalfract6100568Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with PotentialsJiabin Zuo0Zakaria El Allali1Said Taarabti2College of Mathematics, Changchun Normal University, Changchun 130032, ChinaTeam of Modeling and Scientific Computing, LAMAO, Department of Mathematics, Multidisciplinary Faculty of Nador, Mohammed First University, Oujda 60000, MoroccoLISTI, National School of Applied Sciences of Agadir, Ibn Zohr University, Agadir 80000, MoroccoThis paper deals with a fourth-order elliptic equation with Dirichlet boundary conditions. Using a variant form of the mountain pass theorem, we prove the existence of nontrivial solutions to this problem. Furthermore, we discuss the fundamental properties of the representation of the solution by considering two cases. Our results not only make previous results more general but also show new insights into fourth-order elliptic problems.https://www.mdpi.com/2504-3110/6/10/568nontrivial solutionsfourth-ordermountain pass lemmaexistence |
| spellingShingle | Jiabin Zuo Zakaria El Allali Said Taarabti Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials Fractal and Fractional nontrivial solutions fourth-order mountain pass lemma existence |
| title | Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials |
| title_full | Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials |
| title_fullStr | Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials |
| title_full_unstemmed | Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials |
| title_short | Nontrivial Solutions of a Class of Fourth-Order Elliptic Problems with Potentials |
| title_sort | nontrivial solutions of a class of fourth order elliptic problems with potentials |
| topic | nontrivial solutions fourth-order mountain pass lemma existence |
| url | https://www.mdpi.com/2504-3110/6/10/568 |
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