Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations
We study the existence of nontrivial weak solutions for biharmonic equations with Navier and with Dirichlet boundary conditions. This is done by using critical point theory for even functionals, and the theory of strongly monotone operators. Also we analyze the existence of infinitely many weak so...
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| Format: | Article |
| Language: | English |
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Texas State University
2025-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/52/abstr.html |
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| _version_ | 1849341233593319424 |
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| author | Meiqiang Feng Yichen Lu |
| author_facet | Meiqiang Feng Yichen Lu |
| author_sort | Meiqiang Feng |
| collection | DOAJ |
| description | We study the existence of nontrivial weak solutions for biharmonic equations
with Navier and with Dirichlet boundary conditions.
This is done by using critical point theory for even functionals, and
the theory of strongly monotone operators.
Also we analyze the existence of infinitely many weak solutions.
This is probably the first time that the theory of strongly monotone
operator is used to study biharmonic equations. |
| format | Article |
| id | doaj-art-d84216d45d984b64ae07b4d8c86d558c |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-d84216d45d984b64ae07b4d8c86d558c2025-08-20T03:43:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-05-01202552,116Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equationsMeiqiang Feng0Yichen Lu1 Beijing Information Science and Tech. Univ., China Beijing Information Science and Tech. Univ., China We study the existence of nontrivial weak solutions for biharmonic equations with Navier and with Dirichlet boundary conditions. This is done by using critical point theory for even functionals, and the theory of strongly monotone operators. Also we analyze the existence of infinitely many weak solutions. This is probably the first time that the theory of strongly monotone operator is used to study biharmonic equations.http://ejde.math.txstate.edu/Volumes/2025/52/abstr.htmlbiharmonic equationcaratheodory conditions monotone mappingmountain pass lemmaexistence, uniqueness and multiplicity |
| spellingShingle | Meiqiang Feng Yichen Lu Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations Electronic Journal of Differential Equations biharmonic equation caratheodory conditions monotone mapping mountain pass lemma existence, uniqueness and multiplicity |
| title | Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations |
| title_full | Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations |
| title_fullStr | Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations |
| title_full_unstemmed | Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations |
| title_short | Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations |
| title_sort | existence uniqueness and multiplicity of nontrivial solutions for biharmonic equations |
| topic | biharmonic equation caratheodory conditions monotone mapping mountain pass lemma existence, uniqueness and multiplicity |
| url | http://ejde.math.txstate.edu/Volumes/2025/52/abstr.html |
| work_keys_str_mv | AT meiqiangfeng existenceuniquenessandmultiplicityofnontrivialsolutionsforbiharmonicequations AT yichenlu existenceuniquenessandmultiplicityofnontrivialsolutionsforbiharmonicequations |