Stability Conditions of Second Order Integrodifferential Equations with Variable Delay
We investigate integrodifferential functional differential equations ẍ+f(t,x,ẋ)ẋ+∫t-r(t)ta(t,s)g(x(s))ds=0 with variable delay. By using the fixed point theory, we obtain conditions which ensure that the zero solution of this equation is stable under an exponentially weighted metric. Then we est...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/371639 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549017296306176 |
|---|---|
| author | Dingheng Pi |
| author_facet | Dingheng Pi |
| author_sort | Dingheng Pi |
| collection | DOAJ |
| description | We investigate integrodifferential functional differential equations ẍ+f(t,x,ẋ)ẋ+∫t-r(t)ta(t,s)g(x(s))ds=0 with variable delay. By using the fixed point theory, we obtain conditions which ensure that the zero solution of this equation is stable under an exponentially weighted metric. Then we establish necessary and sufficient conditions ensuring that the zero solution is asymptotically stable. We will give an example to apply our results. |
| format | Article |
| id | doaj-art-357a7238677e49158cfb4ca7b67b7f04 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-357a7238677e49158cfb4ca7b67b7f042025-02-03T06:12:24ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/371639371639Stability Conditions of Second Order Integrodifferential Equations with Variable DelayDingheng Pi0School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, ChinaWe investigate integrodifferential functional differential equations ẍ+f(t,x,ẋ)ẋ+∫t-r(t)ta(t,s)g(x(s))ds=0 with variable delay. By using the fixed point theory, we obtain conditions which ensure that the zero solution of this equation is stable under an exponentially weighted metric. Then we establish necessary and sufficient conditions ensuring that the zero solution is asymptotically stable. We will give an example to apply our results.http://dx.doi.org/10.1155/2014/371639 |
| spellingShingle | Dingheng Pi Stability Conditions of Second Order Integrodifferential Equations with Variable Delay Abstract and Applied Analysis |
| title | Stability Conditions of Second Order Integrodifferential Equations with Variable Delay |
| title_full | Stability Conditions of Second Order Integrodifferential Equations with Variable Delay |
| title_fullStr | Stability Conditions of Second Order Integrodifferential Equations with Variable Delay |
| title_full_unstemmed | Stability Conditions of Second Order Integrodifferential Equations with Variable Delay |
| title_short | Stability Conditions of Second Order Integrodifferential Equations with Variable Delay |
| title_sort | stability conditions of second order integrodifferential equations with variable delay |
| url | http://dx.doi.org/10.1155/2014/371639 |
| work_keys_str_mv | AT dinghengpi stabilityconditionsofsecondorderintegrodifferentialequationswithvariabledelay |