Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order
In this paper, we study the existence of nodal solutions of some nonlinear boundary value problems for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. To do this, we first study the global bifurcation of solutions from zero and infinity of the cor...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-06-01
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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=10451 |
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| _version_ | 1841533484036784128 |
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| author | Ziyatkhan Aliyev Yagut Aliyeva |
| author_facet | Ziyatkhan Aliyev Yagut Aliyeva |
| author_sort | Ziyatkhan Aliyev |
| collection | DOAJ |
| description | In this paper, we study the existence of nodal solutions of some nonlinear boundary value problems for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. To do this, we first study the global bifurcation of solutions from zero and infinity of the corresponding nonlinear eigenvalue problems in classes with a fixed oscillation count. Then, using these global bifurcation results, we prove the existence of solutions of the considered nonlinear boundary value problems with a fixed number of nodes. |
| format | Article |
| id | doaj-art-592a75c071be4419a60d1e0c55a52e5e |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-592a75c071be4419a60d1e0c55a52e5e2025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-06-0120242511310.14232/ejqtde.2024.1.2510451Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth orderZiyatkhan Aliyev0https://orcid.org/0000-0001-6923-9288Yagut AliyevaDepartment of Mathematical Analysis, Baku State University, Baku, Azerbaijan & Department of Differential Equations, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, AzerbaijanIn this paper, we study the existence of nodal solutions of some nonlinear boundary value problems for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. To do this, we first study the global bifurcation of solutions from zero and infinity of the corresponding nonlinear eigenvalue problems in classes with a fixed oscillation count. Then, using these global bifurcation results, we prove the existence of solutions of the considered nonlinear boundary value problems with a fixed number of nodes.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10451nonlinear problemeigenvalue parameterbifurcation pointnodal solutioncomponent |
| spellingShingle | Ziyatkhan Aliyev Yagut Aliyeva Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order Electronic Journal of Qualitative Theory of Differential Equations nonlinear problem eigenvalue parameter bifurcation point nodal solution component |
| title | Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order |
| title_full | Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order |
| title_fullStr | Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order |
| title_full_unstemmed | Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order |
| title_short | Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order |
| title_sort | existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order |
| topic | nonlinear problem eigenvalue parameter bifurcation point nodal solution component |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10451 |
| work_keys_str_mv | AT ziyatkhanaliyev existenceofnodalsolutionstosomenonlinearboundaryvalueproblemsforordinarydifferentialequationsoffourthorder AT yagutaliyeva existenceofnodalsolutionstosomenonlinearboundaryvalueproblemsforordinarydifferentialequationsoffourthorder |