Existence and multiplicity results for a coupled system of Kirchhoff type equations
This paper deals with a coupled system of Kirchhoff type equations in ${\mathbb{R}}^{3}$. Under suitable assumptions on the potential functions $V(x)$ and $W(x)$, we obtain the existence and multiplicity of nontrivial solutions when the parameter $\lambda$ is sufficiently large. The method combines...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2014-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2657 |
| _version_ | 1797830676982005760 |
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| author | Dengfeng Lü Jianhai Xiao |
| author_facet | Dengfeng Lü Jianhai Xiao |
| author_sort | Dengfeng Lü |
| collection | DOAJ |
| description | This paper deals with a coupled system of Kirchhoff type equations in ${\mathbb{R}}^{3}$.
Under suitable assumptions on the potential functions $V(x)$ and $W(x)$, we obtain the existence and multiplicity of nontrivial solutions when the parameter $\lambda$ is sufficiently large. The method combines the Nehari manifold and the mountain-pass theorem. |
| first_indexed | 2024-04-09T13:39:53Z |
| format | Article |
| id | doaj.art-d344a2eac7474696a3393e3e0d5254af |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:53Z |
| publishDate | 2014-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-d344a2eac7474696a3393e3e0d5254af2023-05-09T07:53:03ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752014-03-012014611010.14232/ejqtde.2014.1.62657Existence and multiplicity results for a coupled system of Kirchhoff type equationsDengfeng Lü0Jianhai Xiao1School of Mathematics and Statistics, Hubei Engineering University, Hubei 432000, P.R.ChinaSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei 432000, P.R.ChinaThis paper deals with a coupled system of Kirchhoff type equations in ${\mathbb{R}}^{3}$. Under suitable assumptions on the potential functions $V(x)$ and $W(x)$, we obtain the existence and multiplicity of nontrivial solutions when the parameter $\lambda$ is sufficiently large. The method combines the Nehari manifold and the mountain-pass theorem.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2657kirchhoff type equationground state solutionmountain-pass theorem |
| spellingShingle | Dengfeng Lü Jianhai Xiao Existence and multiplicity results for a coupled system of Kirchhoff type equations Electronic Journal of Qualitative Theory of Differential Equations kirchhoff type equation ground state solution mountain-pass theorem |
| title | Existence and multiplicity results for a coupled system of Kirchhoff type equations |
| title_full | Existence and multiplicity results for a coupled system of Kirchhoff type equations |
| title_fullStr | Existence and multiplicity results for a coupled system of Kirchhoff type equations |
| title_full_unstemmed | Existence and multiplicity results for a coupled system of Kirchhoff type equations |
| title_short | Existence and multiplicity results for a coupled system of Kirchhoff type equations |
| title_sort | existence and multiplicity results for a coupled system of kirchhoff type equations |
| topic | kirchhoff type equation ground state solution mountain-pass theorem |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2657 |
| work_keys_str_mv | AT dengfenglu existenceandmultiplicityresultsforacoupledsystemofkirchhofftypeequations AT jianhaixiao existenceandmultiplicityresultsforacoupledsystemofkirchhofftypeequations |