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Diblík, J.; Kúdelčíková, M.

Existence and asymptotic behavior of positive solutions of functional differential equations of delayed type. (English) Zbl 1210.34106

Abstr. Appl. Anal. 2011, Article ID 754701, 16 p. (2011).
Summary: Solutions of the equation
\[ y(t) = - f (t,y_t) \]
are considered for \(t\to \infty\). The existence of two classes of positive solutions which are asymptotically different is proved by using the retract method combined with Razumikhin’s technique. By means of two auxiliary linear equations, which are constructed using upper and lower linear functional estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well.

Cited in 9 Documents

MSC:

34K25 Asymptotic theory of functional-differential equations
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\textit{J. Diblík} and \textit{M. Kúdelčíková}, Abstr. Appl. Anal. 2011, Article ID 754701, 16 p. (2011; Zbl 1210.34106)
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References:

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