Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 104, pp. 1-8.
Title: Boundedness of solutions to fourth-order
differential equation with oscillatory
restoring and forcing terms
Author: Mathew O. Omeike (Univ. of Agriculture, Abeokuta, Nigeria)
Abstract:
This paper concerns the fourth order differential equation
$$
x''''+ax'''+f(x'')+g(x')+h(x)=p(t).
$$
Using the Cauchy formula for the particular solution of
non-homogeneous linear differential equations with constant
coefficients, we prove that the solution and its derivatives
up to order three are bounded.
Submitted February 13, 2007. Published July 30, 2007.
Math Subject Classifications: 34C10, 34C11.
Key Words: Fourth order differential equation; bounded solution;
oscillatory solution; restoring and forcing terms.