PreprintarXiv licencearXiv
Limit theorems for differential systems with multipoint boundary conditions in Sobolev spaces
Abstract
The most general class of multipoint inhomogeneous boundary-value problems for systems of linear ordinary differential equations of arbitrary order r≥ 1 is investigated, whose solutions belong to a given Sobolev space Wpn+r, where n≥ 0 and 1≤ p≤ ∞. The boundary conditions in these problems contain Caputo derivatives of fractional or integer orders, which may exceed the order of the differential system equations. Constructive sufficient conditions are established under which the solutions of these problems are continuous with respect to a parameter from an abstract metric space in the Sobolev space Wpn+r.
Versions
Related
- Existence and multiplicity results for third-order ordinary differential equations with derivative dependence subject to the Riemann–Stieltjes integral boundary conditions
- On a Nonlinear Fractional Delay Differential Equation with Nonlocal Boundary Conditions
- Transversality Conditions for Boundary Constraints Defined by Differential Equations
- Stochastic differential games with random coefficients and state constraints: associated stochastic Hamilton-Jacobi-Bellman-Isaacs equations with Neumann boundary conditions
- Nonlocal Boundary Conditions for Truncated-Fractional Differential Equations Posed on Bounded Domains
BibTeX
@misc{atlasiuk2026limit,
title = {{Limit theorems for differential systems with multipoint boundary conditions in Sobolev spaces}},
author = {Olena Atlasiuk and Vladimir Mikhailets},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.28267},
eprint = {2607.28267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28267},
}
RIS
TY - UNPB
TI - Limit theorems for differential systems with multipoint boundary conditions in Sobolev spaces
AU - Olena Atlasiuk
AU - Vladimir Mikhailets
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.28267
UR - https://arxiv.org/abs/2607.28267
AB - The most general class of multipoint inhomogeneous boundary-value problems for systems of linear ordinary differential equations of arbitrary order r≥ 1 is investigated, whose solutions belong to a given Sobolev space W_p^n+r, where n≥ 0 and 1≤ p≤ ∞. The boundary conditions in these problems contain Caputo derivatives of fractional or integer orders, which may exceed the order of the differential system equations. Constructive sufficient conditions are established under which the solutions of these problems are continuous with respect to a parameter from an abstract metric space in the Sobolev space W_p^n+r.
ER -