International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 3, Pages 269-283
doi:10.1155/S0161171278000307

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

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.