Asymptotic dichotomy in a class of higher order nonlinear delay differential equations
Abstract Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation y(n+2)(t)+p(t)y(n)(t)+q(t)f(y(g(t)))=0 $$ y^{(n+2)}(t)+p(t)y^{(n)}(t)+q(t)f\bigl(y\bigl(g(t)\bigr)\bigr)=0 $$ will converge t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1949-7 |
| _version_ | 1831668774467534848 |
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| author | Yunhua Ye Haihua Liang |
| author_facet | Yunhua Ye Haihua Liang |
| author_sort | Yunhua Ye |
| collection | DOAJ |
| description | Abstract Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation y(n+2)(t)+p(t)y(n)(t)+q(t)f(y(g(t)))=0 $$ y^{(n+2)}(t)+p(t)y^{(n)}(t)+q(t)f\bigl(y\bigl(g(t)\bigr)\bigr)=0 $$ will converge to zero or oscillate, under some conditions listed in the theorems of the present paper. Several examples are also given to illustrate the applications of these results. |
| first_indexed | 2024-12-19T22:47:40Z |
| format | Article |
| id | doaj.art-cc2afd74598d467c851bc8b9fc30a351 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-19T22:47:40Z |
| publishDate | 2019-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-cc2afd74598d467c851bc8b9fc30a3512022-12-21T20:02:55ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-01-012019111710.1186/s13660-018-1949-7Asymptotic dichotomy in a class of higher order nonlinear delay differential equationsYunhua Ye0Haihua Liang1School of Mathematics, Jiaying UniversitySchool of Mathematics and Systems Science, Guangdong Polytechnic Normal UniversityAbstract Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation y(n+2)(t)+p(t)y(n)(t)+q(t)f(y(g(t)))=0 $$ y^{(n+2)}(t)+p(t)y^{(n)}(t)+q(t)f\bigl(y\bigl(g(t)\bigr)\bigr)=0 $$ will converge to zero or oscillate, under some conditions listed in the theorems of the present paper. Several examples are also given to illustrate the applications of these results.http://link.springer.com/article/10.1186/s13660-018-1949-7Asymptotic behaviordelay differential equationhigher order differential equationoscillationSchwarz inequality |
| spellingShingle | Yunhua Ye Haihua Liang Asymptotic dichotomy in a class of higher order nonlinear delay differential equations Journal of Inequalities and Applications Asymptotic behavior delay differential equation higher order differential equation oscillation Schwarz inequality |
| title | Asymptotic dichotomy in a class of higher order nonlinear delay differential equations |
| title_full | Asymptotic dichotomy in a class of higher order nonlinear delay differential equations |
| title_fullStr | Asymptotic dichotomy in a class of higher order nonlinear delay differential equations |
| title_full_unstemmed | Asymptotic dichotomy in a class of higher order nonlinear delay differential equations |
| title_short | Asymptotic dichotomy in a class of higher order nonlinear delay differential equations |
| title_sort | asymptotic dichotomy in a class of higher order nonlinear delay differential equations |
| topic | Asymptotic behavior delay differential equation higher order differential equation oscillation Schwarz inequality |
| url | http://link.springer.com/article/10.1186/s13660-018-1949-7 |
| work_keys_str_mv | AT yunhuaye asymptoticdichotomyinaclassofhigherordernonlineardelaydifferentialequations AT haihualiang asymptoticdichotomyinaclassofhigherordernonlineardelaydifferentialequations |