Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/635926 |
| Summary: | We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |