Stability of delay differential equations with oscillating coefficients
We study the solutions to the delay differential equation equation $$ dot x(t)=-a(t)x(t-h), $$ where the coefficient $a(t)$ is not necessarily positive. It is proved that this equation is exponentially stable provided that $a(t)=b+c(t)$ for some positive constant b less than $pi/(2h)$, and th...
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| Format: | Article |
| Language: | English |
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Texas State University
2010-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/99/abstr.html |
| _version_ | 1818578825314828288 |
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| author | Michael I. Gil' |
| author_facet | Michael I. Gil' |
| author_sort | Michael I. Gil' |
| collection | DOAJ |
| description | We study the solutions to the delay differential equation equation $$ dot x(t)=-a(t)x(t-h), $$ where the coefficient $a(t)$ is not necessarily positive. It is proved that this equation is exponentially stable provided that $a(t)=b+c(t)$ for some positive constant b less than $pi/(2h)$, and the integral $int_0^t c(s)ds$ is sufficiently small for all $t>0$. In this case the 3/2-stability theorem is improved. |
| first_indexed | 2024-12-16T06:51:58Z |
| format | Article |
| id | doaj.art-bef74ff404e746e584cfea05c60d61f5 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-16T06:51:58Z |
| publishDate | 2010-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-bef74ff404e746e584cfea05c60d61f52022-12-21T22:40:22ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-07-01201099,15Stability of delay differential equations with oscillating coefficientsMichael I. Gil'We study the solutions to the delay differential equation equation $$ dot x(t)=-a(t)x(t-h), $$ where the coefficient $a(t)$ is not necessarily positive. It is proved that this equation is exponentially stable provided that $a(t)=b+c(t)$ for some positive constant b less than $pi/(2h)$, and the integral $int_0^t c(s)ds$ is sufficiently small for all $t>0$. In this case the 3/2-stability theorem is improved.http://ejde.math.txstate.edu/Volumes/2010/99/abstr.htmlLinear delay differential equationexponential stability |
| spellingShingle | Michael I. Gil' Stability of delay differential equations with oscillating coefficients Electronic Journal of Differential Equations Linear delay differential equation exponential stability |
| title | Stability of delay differential equations with oscillating coefficients |
| title_full | Stability of delay differential equations with oscillating coefficients |
| title_fullStr | Stability of delay differential equations with oscillating coefficients |
| title_full_unstemmed | Stability of delay differential equations with oscillating coefficients |
| title_short | Stability of delay differential equations with oscillating coefficients |
| title_sort | stability of delay differential equations with oscillating coefficients |
| topic | Linear delay differential equation exponential stability |
| url | http://ejde.math.txstate.edu/Volumes/2010/99/abstr.html |
| work_keys_str_mv | AT michaeligil stabilityofdelaydifferentialequationswithoscillatingcoefficients |