Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 26, pp. 1-5.
Title: Existence of periodic solutions for second-order neutral
differential equations
Author: Yongjin Li (Sun Yat-sen Univ., Guangzhou, China)
Abstract:
By means of variational structure and critical point theory,
we study the existence of periodic solutions for a second-order
neutral differential equation
$$\displaylines{
(p(t) x' (t - \tau ))' + f(t, x(t), x(t-\tau ),
x(t-2\tau) ) = g(t),\cr
x(0) = x(2k\tau), x'(0) = x'(2k\tau).
}$$
where $k$ is a given positive integer and $\tau$ is a positive
number.
Submitted January 6, 2005. Published March 6, 2005.
Math Subject Classifications: 34K13, 34K40, 65K10.
Key Words: Neutral differential equations; periodic solution;
variational method; critical point.