On positive periodic solutions of second order singular equations
Abstract Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations {x¨+a(t)x=f(x),x(0)=x(T),x˙(0)=x˙(T). $$\begin{aligned} \textstyle\begin{cases} \ddot{x}+a(t) x=f(x),\\ x(0)=x(T),\qquad \dot{x}(0)=\dot{x}(T). \...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-1036-5 |
| _version_ | 1811221274155810816 |
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| author | Yunhai Wang Yuanfang Ru |
| author_facet | Yunhai Wang Yuanfang Ru |
| author_sort | Yunhai Wang |
| collection | DOAJ |
| description | Abstract Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations {x¨+a(t)x=f(x),x(0)=x(T),x˙(0)=x˙(T). $$\begin{aligned} \textstyle\begin{cases} \ddot{x}+a(t) x=f(x),\\ x(0)=x(T),\qquad \dot{x}(0)=\dot{x}(T). \end{cases}\displaystyle \end{aligned}$$ For given nonnegative constants 0<β1<β2<⋯<βN $0<\beta_{1}<\beta_{2}<\cdots<\beta_{N}$, the function f may be singular at x=βi $x=\beta_{i}$. |
| first_indexed | 2024-04-12T07:56:30Z |
| format | Article |
| id | doaj.art-712554c28e184669860ee6189fa920ad |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-12T07:56:30Z |
| publishDate | 2018-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-712554c28e184669860ee6189fa920ad2022-12-22T03:41:27ZengSpringerOpenBoundary Value Problems1687-27702018-07-012018111010.1186/s13661-018-1036-5On positive periodic solutions of second order singular equationsYunhai Wang0Yuanfang Ru1School of Mechanical Engineering, Guizhou Institute of TechnologyCollege of Science, China pharmaceutical UniversityAbstract Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations {x¨+a(t)x=f(x),x(0)=x(T),x˙(0)=x˙(T). $$\begin{aligned} \textstyle\begin{cases} \ddot{x}+a(t) x=f(x),\\ x(0)=x(T),\qquad \dot{x}(0)=\dot{x}(T). \end{cases}\displaystyle \end{aligned}$$ For given nonnegative constants 0<β1<β2<⋯<βN $0<\beta_{1}<\beta_{2}<\cdots<\beta_{N}$, the function f may be singular at x=βi $x=\beta_{i}$.http://link.springer.com/article/10.1186/s13661-018-1036-5Periodic solutionsSecond order differential equationsSingularFixed point theorem |
| spellingShingle | Yunhai Wang Yuanfang Ru On positive periodic solutions of second order singular equations Boundary Value Problems Periodic solutions Second order differential equations Singular Fixed point theorem |
| title | On positive periodic solutions of second order singular equations |
| title_full | On positive periodic solutions of second order singular equations |
| title_fullStr | On positive periodic solutions of second order singular equations |
| title_full_unstemmed | On positive periodic solutions of second order singular equations |
| title_short | On positive periodic solutions of second order singular equations |
| title_sort | on positive periodic solutions of second order singular equations |
| topic | Periodic solutions Second order differential equations Singular Fixed point theorem |
| url | http://link.springer.com/article/10.1186/s13661-018-1036-5 |
| work_keys_str_mv | AT yunhaiwang onpositiveperiodicsolutionsofsecondordersingularequations AT yuanfangru onpositiveperiodicsolutionsofsecondordersingularequations |