Geodesic
Functional differential inequalities and estimation of the Cauchy function of an equation with aftereffect
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2014), pp. 52-61

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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.
Keywords: differential inequality, equation with aftereffect, estimate of solution, stability
Mots-clés : test equation. 
@article{IVM_2014_4_a5,
     author = {K. M. Chudinov},
     title = {Functional differential inequalities and estimation of the {Cauchy} function of an equation with aftereffect},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--61},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_4_a5/}
}
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K. M. Chudinov. Functional differential inequalities and estimation of the Cauchy function of an equation with aftereffect. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2014), pp. 52-61. http://geodesic.mathdoc.fr/item/IVM_2014_4_a5/