Factorization method for solving nonlocal boundary value problems in Banach space
| Autor: | I.N. Parasidis, E. Providas |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Қарағанды университетінің хабаршысы. Математика сериясы, Vol 103, Iss 3, Pp 76-86 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2518-7929 2663-5011 |
| DOI: | 10.31489/2021M3/76-86 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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