Electron. J. Diff. Equ., Vol. 2011 (2011), No. 130, pp. 1-7.

Periodic boundary-value problems for fourth-order differential equations with delay

Samuel A. Iyase

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

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Samuel A. Iyase
Department of Mathematics, Computer Science and Information Technology
Igbinedion University, Okada, P.M.B. 0006
Benin City, Edo State, Nigeria
email: driyase2011@yahoo.com, iyasesam@gmail.com

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