A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type
Abstract In this paper, the problem of the existence of periodic solutions is studied for the second-order differential equations with a singularity of repulsive type, x ″ ( t ) + f ( x ′ ( t ) ) + φ ( t ) x ( t ) − 1 x r ( t ) = h ( t ) , $$ x''(t)+f\bigl(x'(t)\bigr)+\varphi(t)x(t)-...
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2017-04-01
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Series: | Advances in Difference Equations |
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Online Access: | http://link.springer.com/article/10.1186/s13662-017-1136-z |
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doaj-5652b0496ff5484cb21b124fce438f4e2020-11-25T00:39:57ZengSpringerOpenAdvances in Difference Equations1687-18472017-04-012017111410.1186/s13662-017-1136-zA new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive typeLijuan Chen0Shiping Lu1College of Math & Statistics, Nanjing University of Information Science & TechnologyCollege of Math & Statistics, Nanjing University of Information Science & TechnologyAbstract In this paper, the problem of the existence of periodic solutions is studied for the second-order differential equations with a singularity of repulsive type, x ″ ( t ) + f ( x ′ ( t ) ) + φ ( t ) x ( t ) − 1 x r ( t ) = h ( t ) , $$ x''(t)+f\bigl(x'(t)\bigr)+\varphi(t)x(t)- \frac{1}{x^{r}(t)}=h(t), $$ where φ and h are T-periodic functions. By using topological degree theory, a new result on the existence of positive periodic solutions is obtained. The interesting thing is that the sign of the function φ ( t ) $\varphi(t)$ is allowed to be changed for t ∈ [ 0 , T ] $t\in[0,T]$ .http://link.springer.com/article/10.1186/s13662-017-1136-zRayleigh equationtopological degreesingularityperiodic solution |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lijuan Chen Shiping Lu |
spellingShingle |
Lijuan Chen Shiping Lu A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type Advances in Difference Equations Rayleigh equation topological degree singularity periodic solution |
author_facet |
Lijuan Chen Shiping Lu |
author_sort |
Lijuan Chen |
title |
A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type |
title_short |
A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type |
title_full |
A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type |
title_fullStr |
A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type |
title_full_unstemmed |
A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type |
title_sort |
new result on the existence of periodic solutions for rayleigh equations with a singularity of repulsive type |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2017-04-01 |
description |
Abstract In this paper, the problem of the existence of periodic solutions is studied for the second-order differential equations with a singularity of repulsive type, x ″ ( t ) + f ( x ′ ( t ) ) + φ ( t ) x ( t ) − 1 x r ( t ) = h ( t ) , $$ x''(t)+f\bigl(x'(t)\bigr)+\varphi(t)x(t)- \frac{1}{x^{r}(t)}=h(t), $$ where φ and h are T-periodic functions. By using topological degree theory, a new result on the existence of positive periodic solutions is obtained. The interesting thing is that the sign of the function φ ( t ) $\varphi(t)$ is allowed to be changed for t ∈ [ 0 , T ] $t\in[0,T]$ . |
topic |
Rayleigh equation topological degree singularity periodic solution |
url |
http://link.springer.com/article/10.1186/s13662-017-1136-z |
work_keys_str_mv |
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