Some quadratic correct extensions of minimal operators in Banach spaces

Parasidis, I. N.; Tsekrekos, P. C.

doi:10.7153/oam-04-11

Cited by 10 publications

(8 citation statements)

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“…The next theorem is analogous to theorem which has been proved in [8] when F 1 , …, F n are linearly independent. This theorem is already proved for the linearly independent set g 1 , …, g n , though using a different method.…”

Section: теоретическая и прикладная математикаmentioning

confidence: 67%

“…This theorem is already proved for the linearly independent set g 1 , …, g n , though using a different method. In addition, it is proved here that the criterion for correctness of the operator B in [8] coincides with the criterion for injectivity of B. Theorem 1. Let X, Y be complex Banach spaces, ˆ: A X Y  be a correct linear operator, the functional vector Fcol(F 1 , …, F n ) [Y  ] n , a vector g(g 1 , …, g n )Y n and g 1 , …, g n is a linearly independent set.…”

Section: теоретическая и прикладная математикаmentioning

confidence: 77%

“…In this setting, problems are often too complex to be solved analytically and therefore numerical solutions are proposed [5,6]. Analytical solutions of a class of boundary value problems, involving the governing differential equation or slight generalizations of the one considered in (1), but with different and/or simpler differential operators, have been proposed in [7][8][9][10]. Existence theorems for nonlocal multipoint boundary value problem and IDEs via analytical methods are given in [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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An exact solution method for Fredholm integro-differential equations

Tsilika

2019

ICS

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Introduction: Linear boundary value problems for Fredholm ordinary integro-differential equations are seldom consideredwith integral boundary conditions in the literature. In our case, integro-differential equations are subject to multipoint or nonlocalintegral boundary conditions. It should be noted that finding exact solutions even for multipoint problems or problems with nonlocalintegral boundary conditions with a differential equation is a difficult task. Purpose: Finding the uniqueness and existencecriterion of solutions for Fredholm ordinary integro-differential equations with multipoint or nonlocal integral boundary conditionsand obtaining exact solutions in closed form of such problems. Results: Within the class of abstract operator equations, for thespecial case of Fredholm integro-differential equations with multipoint or nonlocal integral boundary conditions, a criterion for theexistence and uniqueness of an exact solution is proved and the analytical representation of the solution is given. A direct methodanalytically solving such problems is proposed, in which all calculations are reproducible in any program of symbolic calculations.If the user sets the input parameters and the initial conditions of the problem, the computer codes check the conditions of existenceand uniqueness and of solution generate the analytical solution. The stages of the solution method are illustrated by twoexamples. The article uses computer algebra system Mathematica to demonstrate the results.

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Section: теоретическая и прикладная математикаmentioning

confidence: 67%

Section: теоретическая и прикладная математикаmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

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An exact solution method for Fredholm integro-differential equations

Tsilika

2019

ICS

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“…First we need to find the operators A, A 0 and check the condition D(B 1 ) = D(AA 0 ). If we compare equation (25) with Problem ( 17), (18), it is natural to take…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…The novelty of the factorization method presented here differs from other factorization methods in the literature in the respect that it involves decomposition of both the equation and boundary conditions and delivers the solution in closed form. The technique is new development in Banach spaces and an extension of a procedure used successfully by the authors to solve various other boundary value problems [21][22][23][24] and [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Factorization method for solving nonlocal boundary value problems in Banach space

Parasidis¹,

Providas²

2021

Bul. Kar. Univ. - Math.

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This article deals with the factorization and solution of nonlocal boundary value problems in a Banach space of the abstract form B1u = Au − SΦ(u) − GΨ(A0u) = f, u ∈ D(B1),where A, A0 are linear abstract operators, S, G are vectors of functions, Φ, Ψ are vectors of linear bounded functionals, and u, f are functions. It is shown that the operator B1 under certain conditions can be factorized into a product of two simpler lower order operators as B1 = BB0. Then the solvability and the unique solution of the equation B1u = f easily follow from the solvability conditions and the unique solutions of the equations Bv = f and B0u = v. The universal technique proposed here is essentially different from other factorization methods in the respect that it involves decomposition of both the equation and boundary conditions and delivers the solution in closed form. The method is implemented to solve ordinary and partial Fredholm integro-differential equations.

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