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Oscillation Theory of First Order Differential Equations with Delay


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1 Kanazawa University, Kanazawa 920-1192, Japan
     

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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)ds

and λ1is the smaller root of the equation λ=e


Keywords

Oscillation, First Order Differential Equations, Delay.
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  • Oscillation Theory of First Order Differential Equations with Delay

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Authors

Yutaka Shoukaku
Kanazawa University, Kanazawa 920-1192, Japan

Abstract


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)ds

and λ1is the smaller root of the equation λ=e


Keywords


Oscillation, First Order Differential Equations, Delay.

References