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Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
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M. Ashordia
Published/Copyright:
February 23, 2010
Abstract
Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem
dx(t) = dA(t) · f(t, x(t)),
xi(ti) = ϕi(x) (i = 1, . . . , n),
where 
, A : [a, b] → Rn×n is a matrix-function with bounded variation components, f : [a; b] × Rn → Rn is a vector-function belonging to the Carathéodory class corresponding to A; t1, . . . , tn ∈ [a, b] and ϕ1, . . . , ϕn are the continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation.
Key words and phrases.: Generalized ordinary differential equations; multipoint boundary value problem; solvability; unique solvability
Received: 1995-10-12
Published Online: 2010-02-23
Published in Print: 1998-February
© 1998 Plenum Publishing Corporation
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Articles in the same Issue
- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
- Numerical Solutions to the Darboux Problem with the Functional Dependence
- On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
Keywords for this article
Generalized ordinary differential equations;
multipoint boundary value problem;
solvability;
unique solvability
Articles in the same Issue
- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
- Numerical Solutions to the Darboux Problem with the Functional Dependence
- On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
