International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 727-733

Convergence of the solutions for the equation x(iv)+ax+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x)

Anthony Uyi Afuwape

Department of Mathematics, University of Ife, Ile-lfe, Nigeria

Received 30 May 1984; Revised 26 November 1985

Copyright © 1988 Anthony Uyi Afuwape. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with differential equations of the formx(iv)+ax+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x)where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. By introducing a Lyapunov function, as well as restricting the incrementary ratio η1{h(ζ+η)h(ζ)}, (η0), of h to a closed sub-interval of the Routh-Hurwitz interval, we prove the convergence of solutions for this equation. This generalizes earlier results.