On bounded solutions of linear systems of differential equations with unbounded coefficients
Uteshova R.Ye. Kokotova Ye.V.
2022E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2022#108Issue 4107 - 116 pp.
This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure.
bounded solution , linear system , ordinary differential equation , parameterization method , singular boundary-value problem , unbounded coefficients , well-posedness
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International Information Technology University, Almaty, Kazakhstan
K. Zhubanov Aktobe Regional University, Aktobe, Kazakhstan
International Information Technology University
K. Zhubanov Aktobe Regional University
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