An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation ̇ ð ‘¥ ( ð ‘¡ ) = − ð ‘ ( ð ‘¡ ) ð ‘¥ ( ð ‘¡ − ð œ ( ð ‘¡ ) )

J. Baštinec, J. Diblík and Z. ŠMarda

Abstract and Applied Analysis, 2011, vol. 2011, 1-12

Abstract:

The paper investigates an equation with single delay ̇ ð ‘¥ ( ð ‘¡ ) = − ð ‘ ( ð ‘¡ ) ð ‘¥ ( ð ‘¡ − ð œ ( ð ‘¡ ) ) , where ð œ âˆ¶ [ ð ‘¡ 0 − ð ‘Ÿ , ∞ ) → ( 0 , ð ‘Ÿ ] , ð ‘Ÿ > 0 , ð ‘¡ 0 ∈ â„ , and ð ‘ âˆ¶ [ ð ‘¡ 0 − ð ‘Ÿ , ∞ ) → ( 0 , ∞ ) are continuous functions, and the difference ð ‘¡ − ð œ ( ð ‘¡ ) is an increasing function. Its purpose is to derive a new explicit integral criterion for the existence of a positive solution in terms of ð ‘ and ð œ . An overview of known relevant criteria is provided, and relevant comparisons are also given.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:561902

DOI: 10.1155/2011/561902

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