International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 3, Pages 269-283

Necessary and sufficient conditions for eventually vanishing oscillatory solutions of functional equations with small delays

Bhagat Singh

Department of Mathematics, University of Wisconsin Center, 705 Viebahn Street, Manitowoc 54220, Wisconsin, USA

Received 28 March 1978; Revised 30 June 1978

Copyright © 1978 Bhagat Singh. 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.


Necessary and sufficient conditions are found for all oscillatory solutions of the equation (rn1(t)(rn2(t)((r2(t)(r1(t)y(t))))))+a(t)h(y(g(t)))=b(t) to approach zero. Sufficient conditions are also given to ensure that all solutions of this equation are unbounded.