Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations
The paper studies the existence, exact multiplicity, and a structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega),\ u'(0)=u'(\omega), $$ where $p,f\in L([0,\omega])$ and $q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R...
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-09-01
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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=9185 |
| _version_ | 1797830434047918080 |
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| author | Jiří Šremr |
| author_facet | Jiří Šremr |
| author_sort | Jiří Šremr |
| collection | DOAJ |
| description | The paper studies the existence, exact multiplicity, and a structure of the set of positive solutions to the periodic problem
$$
u''=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega),\ u'(0)=u'(\omega),
$$
where $p,f\in L([0,\omega])$ and $q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R}$ is Carathéodory function. The general results obtained are applied to the forced non-autonomous Duffing equation
$$
u''=p(t)u+h(t)|u|^{\lambda}\operatorname{sgn} u+f(t),
$$
with $\lambda>1$ and a~non-negative $h\in L([0,\omega])$. We allow the coefficient $p$ and the forcing term $f$ to change their signs. |
| first_indexed | 2024-04-09T13:37:12Z |
| format | Article |
| id | doaj.art-54b11a42927d4a22b9ecd992057df3e1 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:12Z |
| publishDate | 2021-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-54b11a42927d4a22b9ecd992057df3e12023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-09-0120216213310.14232/ejqtde.2021.1.629185Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equationsJiří Šremr0Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech RepublicThe paper studies the existence, exact multiplicity, and a structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega),\ u'(0)=u'(\omega), $$ where $p,f\in L([0,\omega])$ and $q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R}$ is Carathéodory function. The general results obtained are applied to the forced non-autonomous Duffing equation $$ u''=p(t)u+h(t)|u|^{\lambda}\operatorname{sgn} u+f(t), $$ with $\lambda>1$ and a~non-negative $h\in L([0,\omega])$. We allow the coefficient $p$ and the forcing term $f$ to change their signs.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9185positive periodic solutionsecond-order differential equationduffing equationexistenceuniquenessmultiplicity |
| spellingShingle | Jiří Šremr Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations Electronic Journal of Qualitative Theory of Differential Equations positive periodic solution second-order differential equation duffing equation existence uniqueness multiplicity |
| title | Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations |
| title_full | Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations |
| title_fullStr | Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations |
| title_full_unstemmed | Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations |
| title_short | Existence and exact multiplicity of positive periodic solutions to forced non-autonomous Duffing type differential equations |
| title_sort | existence and exact multiplicity of positive periodic solutions to forced non autonomous duffing type differential equations |
| topic | positive periodic solution second-order differential equation duffing equation existence uniqueness multiplicity |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9185 |
| work_keys_str_mv | AT jirisremr existenceandexactmultiplicityofpositiveperiodicsolutionstoforcednonautonomousduffingtypedifferentialequations |