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Oscillation Theory of First Order Differential Equations with Delay
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In this paper we try to improve the conditions of [4]. Consequently, we introduce that
L>e-1/e-2(k + 1/λ1) - 1/e-2
is a sufficient condition for the oscillation of all solutions of first order delay differential equation
x′(t) + p(t)x(σ(t)) = 0
under the conditions
L < 1 and 0 < k </1/e,
where k=liminft→∞∫tσ(t) p(s)ds, L=limsupt→∞∫tσ(t)p(s)dsand λ1is the smaller ischolar_main of the equation λ=ekλ
Keywords
Oscillation, First Order Differential Equations, Delay.
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