Asymptotic estimations of the solution for a singularly perturbed equation with unbounded boundary conditions
Atakhan N. Nurpeissov K.S. Konisbayeva K.T.
2022E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2022#108Issue 420 - 30 pp.
The paper studies a two-point boundary value problem with unbounded boundary conditions for a linear singularly perturbed differential equation. Asymptotic estimates are given for a linearly independent system of solutions of a homogeneous perturbed equation. Auxiliary, so-called boundary functions, the Cauchy function are defined. For sufficiently small values of the parameter, estimates for the Cauchy function and boundary functions are found. An algorithm for constructing the desired solution of the boundary value problem has been developed. A theorem on the solvability of a solution to a boundary value problem is proved. For sufficiently small values of the parameter, an asymptotic estimate for the solution of the inhomogeneous boundary value problem is established. The initial conditions for the degenerate equation are determined. The formula is determined; the phenomena of the initial jump are studied.
boundary functions , degenerate problem , initial function , initial jumps , small parameter , two-point boundary value problem
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Zhetysu State University named after I.Zhansugurova, Taldykorgan, Kazakhstan
Al-Farabi Kazakh National University
Zhetysu State University named after I.Zhansugurova
10 лет помогаем публиковать статьи Международный издатель
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