Samandar İSKANDAROV

Article | 2021 | Lobachevskii Journal of Mathematics42 ( 3 )

Sufficient conditions are established such as the sign of the functions of absolute and quadratic integrability on the half-axis of the components of the solution of a linear system of Volterra-type integral equations of the second kind in the new formulation, namely, without the assumption that the components of the free term possess the properties under study. To achieve the intended goals, the matrix method of weight functions, the matrix method of cutting functions, the matrix method of partial cutting of the author, and the method of integral inequalities of Ya. V. Bykov are developed. The results obtained in this paper are gen . . .eralizing for linear scalar and vector integral equations previously considered by the author. Note that some matrix cutting functions introduced introduce a quadratic trinomial of some expressions from the terms of the kernel and the free term in such a way that the core actually absorbs the bad properties of the free term (external force). Note that growth, nonsmoothness, alternating terms of the terms of the kernel and the free term are cut off. It should also be emphasized that the kernel and the free term of the considered system of equations consist additively of two kernels, the terms of the first kernel are cut off by both arguments, the terms of the second kernel are cut off by the second argument, i.e. in part, it is shown that the conditions imposed on these two cores are different, i.e. do not intersect. The introduction of a certain matrix weight function helps to establish the absolute integrability on the half-axis of the solution component of the system under consideration, and it plays a decisive role. At the end, the simplest illustrative example is given, which shows that the results of the present article are also new for the scalar linear integral equation of the Volterra type of the second kind on the semiaxis More less

Asan ÖMÜRALİEV | Peyil Esengul Kızı

Article | 2021 | Lobachevskii Journal of Mathematics42 ( 15 )

The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains boundary layer functions.

Avıt ASANOV | Kalıskan MATANOVA

Article | 2021 | Lobachevskii Journal of Mathematics42 ( 3 )

In this paper, we are applied a new approach to prove that the solution of the linear Fredholm operator equation of the third kind given on a segment and having a finite number of multipoint singularities is equivalent to the solution of the linear Fredholm operator equation of the second kind with additional conditions. We are showed an example of solving the system of linear integral Fredholm equations of the third kind based on the equivalence of the above equations.

Asan ÖMÜRALİEV | Ella ABILAYEVA | Peyil Esengul Kızı

Article | 2020 | Lobachevskii Journal of Mathematics41 ( 1 )

The work is devoted to the construction of the asymptotics of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains, along with parabolic boundary layer functions, and power boundary layer functions.

Fahreddin ABDULLAYEV

Article | 2017 | Lobachevskii Journal of Mathematics38 ( 2 )

In this present work, we continue studying the Nikol’skii and Bernstein–Walsh type estimations for complex algebraic polynomials in the bounded and unbounded regions bounded by asymptotically conformal curve.- Keywords and phrases: Polynomials Nikol’skii inequalities Bernstein inequalities Conformal mapping Asymptotically conformal curve