On Differential Systems in Sobolev spaces with Generic Inhomogeneous Boundary Conditions

2023/04/30 by Olena Atlasiuk, Atlasiuk, Olena, Vladimir Mikhailets +1 · 1 citation
Computer Science · Mathematics · #34B05 #34B08 #34B10 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.00495

openalex publication_date 2023/04/30 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28

Abstract

We study linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general (generic) inhomogeneous boundary conditions in Sobolev spaces. We investigate the character of solvability of inhomogeneous boundary-value problems, prove their Fredholm properties, and find the indices, the dimensions of the kernel, and the cokernel of these problems. Moreover, we obtained necessary and sufficient conditions for continuity in a parameter of solutions to the introduced problems in Sobolev spaces.

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• Parameter-dependent inhomogeneous boundary-value problems in Sobolev spaces

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