Oscillation of second-order Emden-Fowler neutral delay differential equations
In this article, we establish new oscillation criteria for the second-order Emden-Fowler neutral delay differential equation $$ \Big(r(t)|z'(t)|^{\alpha-1}z'(t)\Big)'+q(t)|x(\sigma(t))|^{\beta-1} x\big(\sigma(t)\big)=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)), \alpha>0$ and $\beta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/159/abstr.html |
| _version_ | 1811231109123407872 |
|---|---|
| author | Yingzhu Wu Yuanhong Yu Jinsen Xiao |
| author_facet | Yingzhu Wu Yuanhong Yu Jinsen Xiao |
| author_sort | Yingzhu Wu |
| collection | DOAJ |
| description | In this article, we establish new oscillation criteria for the second-order
Emden-Fowler neutral delay differential equation
$$
\Big(r(t)|z'(t)|^{\alpha-1}z'(t)\Big)'+q(t)|x(\sigma(t))|^{\beta-1}
x\big(\sigma(t)\big)=0,
$$
where $z(t)=x(t)+p(t)x(\tau(t)), \alpha>0$ and $\beta>0$.
Our results improve some well-known results which were published recently
in the literature. Some illustrative examples are also provided to show
the significance of our results. |
| first_indexed | 2024-04-12T10:39:47Z |
| format | Article |
| id | doaj.art-c6fc0eab20d74dee8329be5b5417b197 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T10:39:47Z |
| publishDate | 2018-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c6fc0eab20d74dee8329be5b5417b1972022-12-22T03:36:38ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-09-012018159,115Oscillation of second-order Emden-Fowler neutral delay differential equationsYingzhu Wu0Yuanhong Yu1Jinsen Xiao2 Guangdong Univ. of Petrochemical Tech., Maoming, China Chinese Academy of Sciences, Beijing, China Guangdong Univ. of Petrochemical Tech., Maoming, China In this article, we establish new oscillation criteria for the second-order Emden-Fowler neutral delay differential equation $$ \Big(r(t)|z'(t)|^{\alpha-1}z'(t)\Big)'+q(t)|x(\sigma(t))|^{\beta-1} x\big(\sigma(t)\big)=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)), \alpha>0$ and $\beta>0$. Our results improve some well-known results which were published recently in the literature. Some illustrative examples are also provided to show the significance of our results.http://ejde.math.txstate.edu/Volumes/2018/159/abstr.htmlEmden-Fowler equationhalf-linear differential equationRiccati methodoscillation criterion |
| spellingShingle | Yingzhu Wu Yuanhong Yu Jinsen Xiao Oscillation of second-order Emden-Fowler neutral delay differential equations Electronic Journal of Differential Equations Emden-Fowler equation half-linear differential equation Riccati method oscillation criterion |
| title | Oscillation of second-order Emden-Fowler neutral delay differential equations |
| title_full | Oscillation of second-order Emden-Fowler neutral delay differential equations |
| title_fullStr | Oscillation of second-order Emden-Fowler neutral delay differential equations |
| title_full_unstemmed | Oscillation of second-order Emden-Fowler neutral delay differential equations |
| title_short | Oscillation of second-order Emden-Fowler neutral delay differential equations |
| title_sort | oscillation of second order emden fowler neutral delay differential equations |
| topic | Emden-Fowler equation half-linear differential equation Riccati method oscillation criterion |
| url | http://ejde.math.txstate.edu/Volumes/2018/159/abstr.html |
| work_keys_str_mv | AT yingzhuwu oscillationofsecondorderemdenfowlerneutraldelaydifferentialequations AT yuanhongyu oscillationofsecondorderemdenfowlerneutraldelaydifferentialequations AT jinsenxiao oscillationofsecondorderemdenfowlerneutraldelaydifferentialequations |