On existence of proper solutions of quasilinear second order differential equations
In the paper, the nonlinear differential equation $(a(t)|y^{\prime}|^{p-1}y^{\prime})^{\prime}+b(t)g(y^{\prime})+r(t)f(y)=e(t)$ is studied. Sufficient conditions for the nonexistence of singular solutions of the first and second kind are given. Hence, sufficient conditions for all nontrivial solutio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2007-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=265 |
| _version_ | 1797830763523080192 |
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| author | Miroslav Bartusek E. Pekárková |
| author_facet | Miroslav Bartusek E. Pekárková |
| author_sort | Miroslav Bartusek |
| collection | DOAJ |
| description | In the paper, the nonlinear differential equation $(a(t)|y^{\prime}|^{p-1}y^{\prime})^{\prime}+b(t)g(y^{\prime})+r(t)f(y)=e(t)$ is studied. Sufficient conditions for the nonexistence of singular solutions of the first and second kind are given. Hence, sufficient conditions for all nontrivial solutions to be proper are derived. Sufficient conditions for the nonexistence of weakly oscillatory solutions are given. |
| first_indexed | 2024-04-09T13:41:19Z |
| format | Article |
| id | doaj.art-29807f6c159f4bdcb005af752ad65259 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:19Z |
| publishDate | 2007-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-29807f6c159f4bdcb005af752ad652592023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752007-03-012007511410.14232/ejqtde.2007.1.5265On existence of proper solutions of quasilinear second order differential equationsMiroslav Bartusek0E. Pekárková1Masaryk University, Brno, Czech RepublicMasaryk University, Brno, Czech RepublicIn the paper, the nonlinear differential equation $(a(t)|y^{\prime}|^{p-1}y^{\prime})^{\prime}+b(t)g(y^{\prime})+r(t)f(y)=e(t)$ is studied. Sufficient conditions for the nonexistence of singular solutions of the first and second kind are given. Hence, sufficient conditions for all nontrivial solutions to be proper are derived. Sufficient conditions for the nonexistence of weakly oscillatory solutions are given.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=265 |
| spellingShingle | Miroslav Bartusek E. Pekárková On existence of proper solutions of quasilinear second order differential equations Electronic Journal of Qualitative Theory of Differential Equations |
| title | On existence of proper solutions of quasilinear second order differential equations |
| title_full | On existence of proper solutions of quasilinear second order differential equations |
| title_fullStr | On existence of proper solutions of quasilinear second order differential equations |
| title_full_unstemmed | On existence of proper solutions of quasilinear second order differential equations |
| title_short | On existence of proper solutions of quasilinear second order differential equations |
| title_sort | on existence of proper solutions of quasilinear second order differential equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=265 |
| work_keys_str_mv | AT miroslavbartusek onexistenceofpropersolutionsofquasilinearsecondorderdifferentialequations AT epekarkova onexistenceofpropersolutionsofquasilinearsecondorderdifferentialequations |