Asymptotic behavior of solutions of retarded differential equations
G. Ladas, Y. G. Sficas and I. P. Stavroulakis
Proc. Amer. Math. Soc. 88 (1983), 247-253
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Abstract: In this paper we obtain sufficient conditions under which every solution of the retarded differential equation , where is a nonnegative constant, and , is a continuous function, tends to zero as . Also, under milder conditions, we prove that every oscillatory solution of (1) tends to zero as . More precisely the following theorems have been established.
Theorem 1. Assume that and or . Then every solution of (1) tends to zero as .
Theorem 2. Assume that . Then every oscillatory solution of (1) tends to zero as .
D. Driver, Ordinary and delay differential equations,
Springer-Verlag, New York-Heidelberg, 1977. Applied Mathematical Sciences,
Vol. 20. MR
0477368 (57 #16897)
Ladas, Sharp conditions for oscillations caused by delays,
Applicable Anal. 9 (1979), no. 2, 93–98. MR 539534
- R. D. Driver, Ordinary and delay differential equations, Springer-Verlag, Berlin and New York, 1977. MR 0477368 (57:16897)
- G. Ladas, Sharp conditions for oscillations caused by delays, Applicable Anal. 9 (1979), 93-98. MR 539534 (80h:34094)
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