International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 119-128
doi:10.1155/S0161171292000140
On the oscillatory properties of the solutions of a class of integro-differential equations of neutral type
1P.O. Box 45, Sofia 1504, Bulgaria
2Plovdiv University “Paissii Hilendarski”, Bulgaria
3Moscow Institute of Railway Transport Engineering, Russia
Received 17 January 1990; Revised 6 September 1990
Copyright © 1992 D. D. Bainov et al. 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.
Abstract
In the present paper the oscillatory properties of the solutions of the equation[(Lx)(t)](n)+∫ItK(t,s,x(s))ds=0are investigated where n≥1, L is an operator of the difference type, It⊂ℝ, K:DK→ℝ, DK⫅ℝ3, x:[αx,∞]→ℝ. Under natural conditions imposed on L, It and K it is proved that for n even all ultimately nonzero solutions oscillate and for n odd they either oscillate or tend to zero as t→∞.