Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 130, pp. 1-7.
Title: Periodic boundary-value problems for fourth-order
differential equations with delay
Author: Samuel A. Iyase (Igbinedion Univ., Benin City, Nigeria)
Abstract:
We study the periodic boundary-value problem
$$\displaylines{
x^{(iv)}(t)+f(\ddot{x})\dddot{x}(t)+b\ddot{x}(t)
+g(t,\dot{x}(t-\tau))+dx=p(t)\cr
x(0)=x(2\pi),\quad \dot{x}(0)=\dot{x}(2\pi),\quad
\ddot{x}(0)=\ddot{x}(2\pi),\quad \dddot{x}(0)=\dddot{x}(2\pi),
}$$
Under some resonant conditions on the asymptotic behaviour of the
ratio $g(t,y)/(by)$ for $|y|\to\infty$. Uniqueness of periodic
solutions is also examined.
Submitted June 3, 2011. Published October 11, 2011.
Math Subject Classifications: 34B15.
Key Words: Periodic solution; uniqueness, uniqueness;
Carathoeodory conditions; fourth order ODE; delay