An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)=−c(t)x(t−τ(t))

J. Baštinec, J. Diblík and Z. Šmarda

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: The paper investigates an equation with single delay x.(t)=-c(t)x(t-τ(t)), where τ : [t0 − r, ∞)→(0, r], r > 0, t0 ∈ ℝ, and c : [t0 − r, ∞)→(0, ∞) are continuous functions, and the difference t − τ(t) is an increasing function. Its purpose is to derive a new explicit integral criterion for the existence of a positive solution in terms of c and τ. An overview of known relevant criteria is provided, and relevant comparisons are also given.

Date: 2011
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https://doi.org/10.1155/2011/561902

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:561902

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