On the Solution of Boundary Value Problems for Ordinary Differential Equations of Order n and 2n with General Boundary Conditions

Parasidis, I. N.; Providas, E.; Zaoutsos, Stefanos

doi:10.1007/978-3-030-44625-3_17

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2021

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Cited by 2 publications

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“…Solution formulae to some special boundary value problems for composite differential operators are also obtained. The method is based on the theory of the extensions of linear operators in Banach spaces, see, for example, [33][34][35][36], and is an extension of the work [37] by the authors. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Providas

Zaoutsos

Faraslis

2021

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Section: Introductionmentioning

confidence: 99%

Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Providas

Zaoutsos

Faraslis

2021

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Factorization of Ordinary and Hyperbolic Integro-Differential Equations With Integral Boundary Conditions in a Banach Space

Providas

Пулькина

Parasidis

2021

Vestnik of Samara University. Natural Science Series

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The solvability condition and the unique exact solution by the universal factorization (decomposition) method for a class of the abstract operator equations of the type B1u = Au S(A0u) GF(Au) = f, u D(B1),where A,A0 are linear abstract operators, G, S are linear vectors and , F are linear functional vectors is investigagted. This class is useful for solving Boundary Value Problems (BVPs) with Integro-Differential Equations (IDEs), where A,A0 are differential operators and F(Au), (A0u) are Fredholm integrals. It was shown that the operators of the type B1 can be factorized in the some cases in the product of two moresimple operators BG, BG0 of special form, which are derived analytically. Further the solvability condition and the unique exact solution for B1u = f easily follow from the solvability condition and the unique exact solutions for the equations BGv = f and BG0u = v.

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On the Solution of Boundary Value Problems for Ordinary Differential Equations of Order n and 2n with General Boundary Conditions

Cited by 2 publications

References 9 publications

Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Factorization of Ordinary and Hyperbolic Integro-Differential Equations With Integral Boundary Conditions in a Banach Space

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