Ground state solutions for p-biharmonic equations
In this article we study the p-biharmonic equation $$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$ where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator. When V(x) and f(x,u) satisfy some conditions, we prove that the above equations have Nehari-t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/45/abstr.html |
| _version_ | 1819092432081387520 |
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| author | Xiaonan Liu Haibo Chen Belal Almuaalemi |
| author_facet | Xiaonan Liu Haibo Chen Belal Almuaalemi |
| author_sort | Xiaonan Liu |
| collection | DOAJ |
| description | In this article we study the p-biharmonic equation
$$
\Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N,
$$
where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic
operator. When V(x) and f(x,u) satisfy some conditions, we prove that
the above equations have Nehari-type ground state solutions. |
| first_indexed | 2024-12-21T22:55:31Z |
| format | Article |
| id | doaj.art-2f96dcb3c7944df19fdd6433f1d35809 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T22:55:31Z |
| publishDate | 2017-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-2f96dcb3c7944df19fdd6433f1d358092022-12-21T18:47:27ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-02-01201745,19Ground state solutions for p-biharmonic equationsXiaonan Liu0Haibo Chen1Belal Almuaalemi2 Central South Univ., Changsha, Hunan, China Central South Univ., Changsha, Hunan, China Central South Univ., Changsha, Hunan, China In this article we study the p-biharmonic equation $$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$ where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator. When V(x) and f(x,u) satisfy some conditions, we prove that the above equations have Nehari-type ground state solutions.http://ejde.math.txstate.edu/Volumes/2017/45/abstr.htmlp-biharmonic equationsNehari manifoldground state solution |
| spellingShingle | Xiaonan Liu Haibo Chen Belal Almuaalemi Ground state solutions for p-biharmonic equations Electronic Journal of Differential Equations p-biharmonic equations Nehari manifold ground state solution |
| title | Ground state solutions for p-biharmonic equations |
| title_full | Ground state solutions for p-biharmonic equations |
| title_fullStr | Ground state solutions for p-biharmonic equations |
| title_full_unstemmed | Ground state solutions for p-biharmonic equations |
| title_short | Ground state solutions for p-biharmonic equations |
| title_sort | ground state solutions for p biharmonic equations |
| topic | p-biharmonic equations Nehari manifold ground state solution |
| url | http://ejde.math.txstate.edu/Volumes/2017/45/abstr.html |
| work_keys_str_mv | AT xiaonanliu groundstatesolutionsforpbiharmonicequations AT haibochen groundstatesolutionsforpbiharmonicequations AT belalalmuaalemi groundstatesolutionsforpbiharmonicequations |