Functional differential inequalities and estimation of the Cauchy function of an equation with aftereffect

K. M. Chudinov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2014), pp. 52-61.

Résumé

We consider scalar functional differential inequalities that are used to estimate solutions of differential equations with deviating argument. A theorem on positiveness of the Cauchy function of a differential equation with aftereffect is derived from a theorem on a functional differential inequality with nonlinear monotone operator, which is a direct generalization of the simplest classical theorem on a differential inequality. The suggested proofs rely on local properties of continuous functions, only.

Détail

Keywords: differential inequality, equation with aftereffect, estimate of solution, stability
Mots-clés : test equation.

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