Conditions for the absence of positive solutions of a first order differential inequality with a single delay. (English) Zbl 0849.34054

Kozakiewicz, Erwin

Arch. Math., Brno 31, No. 4, 291-297 (1995).

The author proves a sufficient integral condition for the absence of eventually positive solutions of a first order stable type differential inequality with one nondecreasing retarded argument. In the special case of equality the result becomes an oscillation criterion.

Reviewer: V.Lakshmikantham (Melbourne/Florida)

MSC:

34K11	Oscillation theory of functional-differential equations
34A40	Differential inequalities involving functions of a single real variable
34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

positive solutions; differential inequality with one nondecreasing retarded argument; oscillation criterion