New general solution of a family higher order differential equations and its application to solve multipoint-integral problems

Abstract

The family multipoint-integral problems of higher order differential equations is considered.An effective method for solving to family multipoint-integral problems for higher order differential equations is offered. A domain is divided into m parts, the values of a solution at the beginning lines of the subdomains are considered as functional parameters, and the family higher order differential equations are reduced to the family Cauchy problems on the subdomains for
system of differential equations with functional parameters. Using the solutions to these family problems, new general solutions to family higher order differential equations are introduced and their properties are established. Based on the general solution, family multipoint-integral problems, and continuity conditions of a solution at the interior lines of the partition, the linear system of functional equations with respect to parameters is composed. Algorithms for finding solutions to families of multipoint-integral problems for higher order differential equations are constructed and conditions for unique solvability are established in the terms of initial data.