Electron. J. Diff. Eqns., Vol. 2005(2005), No. 26, pp. 1-5.

Existence of periodic solutions for second-order neutral differential equations

Yongjin Li

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.

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Yongjin Li
Department of Mathematics
Sun Yat-sen University
Guangzhou, 510275, China
email: stslyj@zsu.edu.cn

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