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). $$\begin{aligned} \textstyle\begin{cases} \ddot{x}+a(t) x=f(x),\\ x(0)=x(T),\qquad \dot{x}(0)=\dot{x}(T). \...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-1036-5 |
| Summary: | Abstract Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations {x¨+a(t)x=f(x),x(0)=x(T),x˙(0)=x˙(T). $$\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 $x=\beta_{i}$. |
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| ISSN: | 1687-2770 |