ON THE UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATIONS WITH PARAMETER
ПАРАМЕТРІ БАР ДИФФЕРЕНЦИАЛДЫҚ ТЕҢДЕУ ҮШІН ШЕТТІК ЕСЕПТІҢ БІРМӘНДІ ШЕШІЛІМДІЛІГІ ТУРАЛЫ
ОБ ОДНОЗНАЧНОЙ РАЗРЕШИМОСТИ КРАЕВОЙ ЗАДАЧИ ДЛЯ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ С ПАРАМЕТРОМ
Bakirova E.A. Iskakova N.B. Тemesheva S.М. Каdirbayeva Zh.М.
2024Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2024#21Issue 164 - 74 pp.
A linear boundary value problem for a differential equation with a parameter is investigated on a finite interval by the parameterization method. The studied boundary value problem with parameter is reduced to an equivalent multipoint boundary value problem with parameters by splitting the interval, introducing additional parameters at the points of splitting and new functions. The obtained equivalent boundary value problem contains Cauchy problems for ordinary differential equations with respect to new functions. By substituting the solution representation of the Cauchy problem into the boundary conditions and continuity conditions of the solution, a system of linear algebraic equations with respect to the introduced parameters is compiled. An algorithm for finding a solution to the boundary value problem with parameters is constructed. The formulation of the theorem on sufficient conditions of unique solvability of the boundary value problem with parameters is given. Sufficient conditions of its unique solvability are obtained in terms of the data of the original boundary value problem. An example showing the fulfillment of the conditions of the theorem is given.
boundary value problem , differential equation with parameter , parameterization method , solvability
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakh National Womens Teacher Training University, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan
International Information Technology University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Kazakh National Womens Teacher Training University
Al-Farabi Kazakh National University
International Information Technology University
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