Asymptotic behavior of solutions to higher order nonlinear delay differential equations
In this article, we study the oscillation and asymptotic behavior of solutions to the nonlinear delay differential equation $$ x^{(n+3)}(t)+p(t)x^{(n)}(t)+q(t)f(x(g(t)))=0. $$ By using a generalized Riccati transformation and an integral averaging technique, we establish sufficient condition...
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Texas State University
2014-09-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/186/abstr.html |
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doaj-894a31073c3e4c979e8d4c351e473adb2020-11-24T23:34:53ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-09-012014186,112Asymptotic behavior of solutions to higher order nonlinear delay differential equationsHaihua Liang0 Guangdong Polytechnic Normal Univ., Guangdong, China In this article, we study the oscillation and asymptotic behavior of solutions to the nonlinear delay differential equation $$ x^{(n+3)}(t)+p(t)x^{(n)}(t)+q(t)f(x(g(t)))=0. $$ By using a generalized Riccati transformation and an integral averaging technique, we establish sufficient conditions for all solutions to oscillate, or to converge to zero. Especially when the delay has the form $g(t)=at-\tau$, we provide two convenient oscillatory criteria. Some examples are given to illustrate our results.http://ejde.math.txstate.edu/Volumes/2014/186/abstr.htmlHigher order differential equationdelay differential equation, asymptotic behavioroscillation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Haihua Liang |
| spellingShingle |
Haihua Liang Asymptotic behavior of solutions to higher order nonlinear delay differential equations Electronic Journal of Differential Equations Higher order differential equation delay differential equation, asymptotic behavior oscillation |
| author_facet |
Haihua Liang |
| author_sort |
Haihua Liang |
| title |
Asymptotic behavior of solutions to higher order nonlinear delay differential equations |
| title_short |
Asymptotic behavior of solutions to higher order nonlinear delay differential equations |
| title_full |
Asymptotic behavior of solutions to higher order nonlinear delay differential equations |
| title_fullStr |
Asymptotic behavior of solutions to higher order nonlinear delay differential equations |
| title_full_unstemmed |
Asymptotic behavior of solutions to higher order nonlinear delay differential equations |
| title_sort |
asymptotic behavior of solutions to higher order nonlinear delay differential equations |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2014-09-01 |
| description |
In this article, we study the oscillation and asymptotic behavior of solutions
to the nonlinear delay differential equation
$$
x^{(n+3)}(t)+p(t)x^{(n)}(t)+q(t)f(x(g(t)))=0.
$$
By using a generalized Riccati transformation and an integral averaging technique,
we establish sufficient conditions for all solutions to oscillate, or to
converge to zero. Especially when the delay has the form $g(t)=at-\tau$,
we provide two convenient oscillatory criteria.
Some examples are given to illustrate our results. |
| topic |
Higher order differential equation delay differential equation, asymptotic behavior oscillation |
| url |
http://ejde.math.txstate.edu/Volumes/2014/186/abstr.html |
| work_keys_str_mv |
AT haihualiang asymptoticbehaviorofsolutionstohigherordernonlineardelaydifferentialequations |
| _version_ |
1725527196703916032 |