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Zbl 0930.34050
Kordonis, I.-G.E.; Philos, Ch.G.
Oscillation and nonoscillation in delay or advanced differential equations and in integrodifferential equations.
(English)
[J] Georgian Math. J. 6, No.3, 263-284 (1999). ISSN 1072-947X; ISSN 1572-9176/e

New sufficient conditions are obtained for the oscillation of all solutions to a class of linear homogeneous first-order delay/advanced differential equations with variable coefficients and variable delays or advanced arguments. The existence of positive solutions is discussed for such delay/advanced equations under certain conditions. Necessary conditions are derived on certain homogeneous linear first-order integrodifferential equations to have positive solutions. Sufficient conditions are given for the existence of positive solutions which tend to zero as $t\to\infty$ for such integrodifferential equations.
[N.Parhi (Berhampur)]
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
45J05 Integro-ordinary differential equations

Keywords: oscillation; nonoscillation; delay/advanced differential equations; existence; positive solutions

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