Abstract
This article is an immediate continuation of [1]. Solution of the Lyapunov equation leads to a boundary value problem for the first-order hyperbolic equations in two variables with data on the boundary of the unit square. In general, the problems of this kind are not normally solvable. We prove that the boundary value problems in question possess the Fredholm property under some conditions.
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Skazka V. V., “On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. I. Solvability of the Lyapunov equation,” Siberian Math. J., 37, No.3, 573–590 (1996).
Sobolev S. L., Equations of Mathematical Physics [in Russian], OGIZ, Moscow; Leningrad (1947).
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Original Russian Text Copyright © 2005 Skazka V. V.
The author was supported by the Integration Grant of the Siberian Division of the Russian Academy of Sciences, 2000 (No. 103), the Presidium of the Russian Academy of Sciences (Program No. 16, Project 115), and the Russian Foundation for Basic Research (Grant 03-01-00162).
In memory of Tadei Ivanovich Zelenyak.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 1163–1178, September– October, 2005.
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Skazka, V.V. On Counting the Number of Eigenvalues in the Right Half-Plane for Spectral Problems Connected with Hyperbolic Systems. II. Differential Equations. Sib Math J 46, 935–947 (2005). https://doi.org/10.1007/s11202-005-0090-2
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DOI: https://doi.org/10.1007/s11202-005-0090-2