On the unique solvability of a family of multipoint-integral boundary value problems for a third order differential equation

A. T. Assanova, Askarbek E. Imanchiyev

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2018

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DOI 10.31489/2018m2/25-33
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Abstract

On the unique solvability of a family of multipoint-integral boundary value problems for a third order differential equation A family multipoint-integral boundary value problems for a third order differential equation with variable coefficients is considered.The questions of a existence unique solution of the considered problem and ways of its construction are investigated.The family multipoint-integral boundary value problems for the differential equation of third order with variable coefficients is reduced to a family multipoint-integral boundary value problems for a system of three differential equations by introducing new functions.For solve of resulting family of multipoint-integral boundary value problems is applied a parametrization method.An algorithms of finding the approximate solution to the family multipoint-integral boundary value problems for the system of three differential equations are proposed and their convergence is proved.The conditions of the unique solvability of the family multipoint-integral boundary value problems for the system of three differential equations are obtained in the terms of initial data.The results also formulated relative to the original of the family multipoint-integral boundary value problems for the differential equation of third order with variable coefficients.