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

Singh, Bhagat

doi:https://doi.org/10.1155/S0161171278000307

International Journal of Mathematics and Mathematical Sciences

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Volume 1 | Article ID 637068 | https://doi.org/10.1155/S0161171278000307

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

Bhagat Singh¹

Received28 Mar 1978

Revised30 Jun 1978

Abstract

Necessary and sufficient conditions are found for all oscillatory solutions of the equation (rn−1(t)(rn−2(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.

Copyright

Copyright © 1978 Hindawi Publishing Corporation. 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.

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