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Ordinary differential equations with power boundary layers

Asan ÖMÜRALİEV | Ella ABILAYEVA

The regularized asymptotics of a solution of the Cauchy problem for systems of singularly perturbed ordinary differential equations is constructed. It is shown that a power boundary layer appears in such problems in addition to other boundary layers.

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Regularization of the Singularly Perturbed Cauchy Problem for a Hyperbolic System

Asan ÖMÜRALİEV | Ella ABILAYEVA

In this paper we construct the asymptotics of the solution of the Cauchy problem for a singularly perturbed hyperbolic system by using the regularization method for singularly perturbed problems of S.A. Lomov. The regularization method for singularly perturbed problems of S.A. Lomov is used for the first time to construct the asymptotic solution of a hyperbolic system.

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On the recursive sequence xn+1=xn−(4k+3)1+∏t=02xn−(k+1)t−k

Dağıstan ŞİMŞEK | Fahreddin ABDULLAYEV

The solution of the difference equation (Formula presented.),..., where x−(4k+3), x−(4k+2),..., x−1, x0 ∈ (0, ∞) and k = 0, 1,..., is studied.

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Singularly Perturbed System of Parabolic Equations in the Critical Case

Asan ÖMÜRALİEV

We examine a system of singularly perturbed parabolic equations in the case where the small parameter is involved as a coefficient of both time and spatial derivatives and the spectrum of the limit operator has a multiple zero point. In such problems, corner boundary layers appear, which can be described by products of exponential and parabolic boundary-layer functions. Under the assumption that the limit operator is a simple-structure operator, we construct a regularized asymptotics of a solution, which, in addition to corner boundary-layer functions, contains exponential and parabolic boudar ...More

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Bernstein–Walsh type inequalities in unbounded regions with piecewise asymptotically conformal curve in the weighted Lebesgue space

Meerim İmaş Kızı | Fahreddin ABDULLAYEV

We have obtained the pointwise Bernstein–Walsh type estimation for algebraic polynomials in the unbounded regions with piecewise asymptotically conformal boundary, having exterior and interior zero angles, in the weighted Lebesgue space.

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On the Recursive Sequence xn+1=xn−(k+1)1+xnxn−1…xn−k

Dağıstan ŞİMŞEK

A solution of the following difference equation is investigated:xn+1=xn−(k+1)1+xnxn−1…xn−k,n=0,1,2,… where x−(k+1); x−k; : : : ; x−1; x0 𝜖 (0;∞) and k = 0; 1; 2; : : :.

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