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: (x) over dot(t) = -f(t, x(t - r)) and (x) over dot(t) = -f(t, x(t - s)) - f(t, x(t - 2s)), where f is an element of C(R x 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.