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References (13)
-
N.A. Izobov (1997)
The existence of linear Pfaff systems whose set of lower characteristic vectors has a positive plane measureDiffer. Equations, 33
-
(1966)
Translated under the title Topologicheskie vektornye prostranstva -
(1976)
Characteristic vectors and sets of functions of two variables and their basic properties -
H.H. Schaefer (1971)
Topological Vector Spaces -
(1989)
Lineinye uravneniya v polnykh differentsialakh (Linear Total Differential Equations) -
P. Lax, H. Grossman, G. Avila (1959)
Theory of functions of a real variable -
(1998)
Construction of a linear Pfaff equation with arbitrarily prescribed characteristic and lower characteristic sets -
A. Platonov, S. Krasovskii (2016)
Existence of a linear Pfaff system with arbitrary bounded disconnected lower characteristic set of positive Lebesgue m-measureDifferential Equations, 52
-
N. Izobov, S. Krasovskii, A. Platonov (2008)
Existence of linear Pfaffian systems whose lower characteristic set has positive measure in R3Differential Equations, 44
-
I.P. Natanson (1974)
Teoriya funktsii veshchestvennoi peremennoi (Theory of Functions of a Real Variable) -
(1976)
Elementy teorii funktsii i funktsional’nogo analiza (Elements of Function Theory and Functional Analysis) -
(1966)
Topological Vector Spaces, New York: Macmillan -
(1983)
Vpolne razreshimye mnogomernye differentsial’nye uravneniya (Completely Solvable Multidimensional Differential Equations)
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266117100020
- Publisher site
- See Article on Publisher Site
Abstract
For any positive integers n ≥ 1 and m ≥ 2, we give a constructive proof of the existence of linear n-dimensional Pfaff systems with m-dimensional time and with infinitely differentiable coefficient matrices such that the characteristic and lower characteristic sets of these systems are given sets that are the graphs of a concave continuous function and a convex continuous function, respectively, defined and monotone decreasing on simply connected closed bounded convex domains of the space ℝ m−1.
Journal
Differential Equations – Springer Journals
Published: Nov 25, 2017