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Article

Kozakiewicz, Erwin
Conditions for the absence of positive solutions of a first order differential inequality with a single delay. (English). Archivum Mathematicum, vol. 31 (1995), issue 4, pp. 291-297
MSC: 34A40, 34C10, 34K05, 34K11 | MR 1390588 | Zbl 0849.34054
Keywords:
delay; differential inequality; oscillation
Summary:
A sufficient integral condition for the absence of eventually positive solutions of a first order stable type differential inequality with one nondecreasing retarded argument is given. In the special case of equality the result becomes an oscillation criterion.
References:
[1] Ladde G.S., Lakshmikantham V., Zhang B.G.: Oscillation Theory of Differential Equations with Deviating Arguments. Marcel Dekker, New York, 1987. MR 1017244 | Zbl 0832.34071
[2] Kozakiewicz E.: Oscillations for First Order Neutral Differential Equations. ZAMM 73 (1993), T813-T815. MR 1237876 | Zbl 0815.34062
[3] Kozakiewicz E.: Conditions for the absence of positive solutions of first order differential inequalities with deviating arguments. 4th. Int. Coll. on Differential Equations, pp. 157-161, D. Bainov and V. Covachev (eds.), VSP 1994. MR 1458394 | Zbl 0843.34071
[4] Elbert Á., Stavroulakis I.P.: Oscillation and Non-oscillation Criteria for Delay Differential Equations. Proc. Amer. Math. Soc., 123 (1995), 1503-1510, or University of Ioannina, Greece, Technical Report No. 228, July 1993. MR 1242082
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