A two-point boundary-value problem for a singularly perturbed linear system of differential equations

1978 ◽  
Vol 29 (4) ◽  
pp. 385-388
Author(s):  
M. At. Arolska ◽  
D. D. Bainov
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
System Of Differential Equations

Matrix boundary-value problems for differential equations with p-Laplacian

2020 ◽  
Vol 17 (1) ◽  
pp. 41-57
Author(s):  
Olga Nesmelova
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Arbitrary Function ◽  
Algebraic System ◽  
Boundary Value ◽  
System Of Differential Equations ◽  
Differential Algebraic System ◽  
Uniqueness Of The Solution

We consider the boundary-value problem for a linear system of differential equations with matrix p-Laplacian, which is reduced to the traditional differential-algebraic system with an unknown in the form of the vector function. A generalization of various boundary-value problems for differential equations with p-Laplacian, which preserves the features of the solution of such problems, namely, the lack of uniqueness of the solution and, in this case, the dependence of the desired solution on an arbitrary function, is given.

scholarly journals ON A TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH MANY TRANSFORMED ARGUMENTS

2021 ◽  
Vol 9 (1) ◽  
pp. 284-290
Author(s):  
M. Filipchuk
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Method ◽  
Point Boundary ◽  
System Of Differential Equations ◽  
Actual Problem ◽  
Approximate Construction ◽  
Transformed Arguments

A.M. Samoilenko’s numerical-analytic method is a well-known and effective research method of solvability and approximate construction of the solutions of various boundary value problems for systems of differential equations. The investigation of boundary value problems for new classes of systems of functional- differential equations by this method is still an actual problem. A boundary value problem for a system of differential equations with finite quantity of transformed arguments in the case of linear two-point boundary conditions is considered at this paper. In order to study the questions of the existence and approximate construction of a solution of this problem, we used a modification of A.M. Samoilenko’s numerical-analytic method without determining equation, i.e. the method has an analytical component only. Sufficient conditions for the existence of a unique solution of the considered boundary value problem and an error estimation of the constructed successive approximations are obtained. The use of the developed modification of the method is illustrated by concrete examples.

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