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 ℝm−1.
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Original Russian Text © A.S. Platonov, S.G. Krasovskii, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 10, pp. 1290–1297.
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Platonov, A.S., Krasovskii, S.G. Construction of a linear Pfaff system with m-dimensional time and with given characteristic set and lower characteristic set. Diff Equat 53, 1254–1261 (2017). https://doi.org/10.1134/S0012266117100020
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DOI: https://doi.org/10.1134/S0012266117100020