Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime
In this paper, we consider the radially symmetric spacelike solutions of a nonlinear Dirichlet problem for the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime. By using a conformal change of variable, this problem can be translated an equivalent proble...
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University of Szeged
2024-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10846 |
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| _version_ | 1850090784177520640 |
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| author | Ting Wang Man Xu |
| author_facet | Ting Wang Man Xu |
| author_sort | Ting Wang |
| collection | DOAJ |
| description | In this paper, we consider the radially symmetric spacelike solutions of a nonlinear Dirichlet problem for the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime. By using a conformal change of variable, this problem can be translated an equivalent problem in the Minkowski spacetime. By using the lower and upper solution method, fixed point, a priori bounds and topological degree method, we obtain the existence, nonexistence and multiplicity of radially symmetric spacelike solutions. |
| format | Article |
| id | doaj-art-def08de5f8e44c88bb38f1de05d29da6 |
| institution | DOAJ |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-def08de5f8e44c88bb38f1de05d29da62025-08-20T02:42:30ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-03-0120241611910.14232/ejqtde.2024.1.1610846Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetimeTing Wang0Man XuCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, P.R. ChinaIn this paper, we consider the radially symmetric spacelike solutions of a nonlinear Dirichlet problem for the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime. By using a conformal change of variable, this problem can be translated an equivalent problem in the Minkowski spacetime. By using the lower and upper solution method, fixed point, a priori bounds and topological degree method, we obtain the existence, nonexistence and multiplicity of radially symmetric spacelike solutions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10846topological degreeradially symmetric spacelike solutionsdirichlet problemprescribed mean curvature spacelike equationfriedmann–lemaître–robertson–walker spacetime |
| spellingShingle | Ting Wang Man Xu Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime Electronic Journal of Qualitative Theory of Differential Equations topological degree radially symmetric spacelike solutions dirichlet problem prescribed mean curvature spacelike equation friedmann–lemaître–robertson–walker spacetime |
| title | Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime |
| title_full | Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime |
| title_fullStr | Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime |
| title_full_unstemmed | Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime |
| title_short | Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime |
| title_sort | multiple positive radial solutions for dirichlet problem of the prescribed mean curvature spacelike equation in a friedmann lemaitre robertson walker spacetime |
| topic | topological degree radially symmetric spacelike solutions dirichlet problem prescribed mean curvature spacelike equation friedmann–lemaître–robertson–walker spacetime |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10846 |
| work_keys_str_mv | AT tingwang multiplepositiveradialsolutionsfordirichletproblemoftheprescribedmeancurvaturespacelikeequationinafriedmannlemaitrerobertsonwalkerspacetime AT manxu multiplepositiveradialsolutionsfordirichletproblemoftheprescribedmeancurvaturespacelikeequationinafriedmannlemaitrerobertsonwalkerspacetime |