To the boundary value problem of ordinary differential equations

Aisagaliev, S. A.; Zhunussova, Zhanat

doi:10.14232/ejqtde.2015.1.57

Cited by 3 publications

(6 citation statements)

References 1 publication

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“…This is the principal difference of the proposed method in comparison with known methods. This work is a continuation of the studies presented in [6][7][8][9][10][11][12].…”

Section: Formulation Of the Problemmentioning

confidence: 64%

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To the solution of a boundary value problem with a parameter for an ordinary differential equations

Aisagaliev¹,

Zhunusova²

2016

Ufimskii Matematicheskii Zhurnal

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We propose a method for solving a boundary value problem with a parameter under the presence of constraints for state and integral constraints. We obtain the necessary and sufficient conditions solvability for the boundary value problem with a parameter for ordinary differential equations. A method for constructing the solution to the boundary value problem with a parameter and constraints is developed by constructing minimizing sequences. The basis of the proposed method for solving the boundary value problem is the immersion principle. The immersion principle is created by finding the general solution for a class of the first kind Fredholm integral equations. As an example, the solution of the Sturm-Liouville problem for a parameter value in a prescribed interval is given.A.S. Aisagaliev, Zh.Kh. Zhunussova, To the solution of the boundary value problem with a parameter for ordinary differential equations.

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“…This is the principal difference of the proposed method in comparison with known methods. This work is a continuation of the studies presented in [6][7][8][9][10][11][12].…”

Section: Formulation Of the Problemmentioning

confidence: 64%

“…The proof of Theorems 1, 2 was given in works [6,7]. Application of Theorems 1, 2 to control problems was presented in [8][9][10], while the boundary value problems for ordinary differential equations were discussed in [11,12].…”

Section: Immersion Principlementioning

confidence: 99%

To the solution of a boundary value problem with a parameter for an ordinary differential equations

Aisagaliev¹,

Zhunusova²

2016

Ufimskii Matematicheskii Zhurnal

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“…This work is a continuation of scientific research from [12] [17]- [23]. The scientific novelty of the results obtained in this article is the reduction of solvability and construction of a solution of the Fredholm integral equation of the first kind to an extremal problem in Hilbert space; construction of minimizing sequences and studies of their convergence; determination of weak limit points of minimizing sequences; creation of constructive theory of solvability and construction of solutions of integrodifferential equations with distributed delay in control.…”

Section: Introductionmentioning

confidence: 92%

“…A review of scientific research on differential equations with deviating arguments is contained in [11]. A qualitative theory of integrodifferential equations is presented in [12]. A review of numerical methods for solving integrodifferential equations can be found in [13].…”

Section: Introductionmentioning

confidence: 99%

Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

Serikbai,

Dias,

Ilya

2024

JAMP

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The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

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“…Applications of Theorems 1 and 2 to the solution of controllability and optimal control problems are described in [4][5][6][7].…”

Section: Theoremmentioning

confidence: 99%

Constructive method for solving a boundary value problem for ordinary differential equations

Aisagaliev

Калимолдаев

2015

Diff Equat

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We suggest a method for solving a boundary value problem for ordinary differential equations with boundary conditions in the presence of state and integral constraints. The method is based on the embedding principle, which permits one to reduce the original boundary value problem to a special optimal control problem with the use of the general solution of a Fredholm integral equation of the first kind. STATEMENT OF THE PROBLEMConsider the boundary value probleṁwith the boundary conditionsthe phase constraintsand the integral constraintsHere A(t) and B(t) are given n × n and n × m matrices, respectively, with piecewise continuous entries, μ(t), t ∈ I, is a given n-dimensional vector function with piecewise continuous components, f (x, t) is an m-dimensional vector function that is jointly continuous with respect to the variables (x, t) ∈ R n × I and satisfies the conditionsand S is a given convex closed set. The function F (x, t) = (F 1 (x, t), . . . , F r (x, t)), t ∈ I, is an r-dimensional jointly continuous vector function, and γ(t) = (γ 1 (t), . . . , γ r (t)) and δ(t) = (δ 1 (t), . . . , δ r (t)), t ∈ I, are given continuous functions.149

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To the boundary value problem of ordinary differential equations

Cited by 3 publications

References 1 publication

To the solution of a boundary value problem with a parameter for an ordinary differential equations

To the solution of a boundary value problem with a parameter for an ordinary differential equations

Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

Constructive method for solving a boundary value problem for ordinary differential equations

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