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Ordinary differential equations with point interactions: An inverse problem
- Source :
- J. Math. Anal. Appl. 471 (2019) 53 - 72
- Publication Year :
- 2018
-
Abstract
- Given a linear ordinary differential equation (ODE) on $\RE$ and a set of interface conditions at a finite set of points $I \subset \RE$, we consider the problem of determining another differential equation whose {\it global} solutions satisfy the original ODE on $\RE \backslash I $, and the interface conditions at $I $. Using an extension of the product of distributions with non-intersecting singular supports presented in [L. H\"ormander, The Analysis of Linear Partial Diffe\-rential Operators I, Springer-Verlag, 1983], we determine an {\it intrinsic} solution of this problem, i.e. a new ODE, satisfying the required conditions, and strictly defined within the space of Schwartz distributions. Using the same formalism, we determine a singular perturbation formulation for the $n$-th order derivative operator with interface conditions.<br />Comment: 23 pages, to appear in J. Math Anal. Appl
- Subjects :
- Mathematics - Functional Analysis
Mathematics - Classical Analysis and ODEs
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Math. Anal. Appl. 471 (2019) 53 - 72
- Publication Type :
- Report
- Accession number :
- edsarx.1811.01083
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jmaa.2018.10.061