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On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. II: Differential equations. (Russian, English) Zbl 1119.35038

Sib. Mat. Zh. 46, No. 5, 1163-1178 (2005); translation in Sib. Math. J. 46, No. 5, 935-947 (2005).
Summary: This article is an immediate continuation of the author’s paper [Sib. Math. J. 37, No. 3, 573–590 (1996; Zbl 0887.35112)]. The solution of the Lyapunov equation leads to a boundary value problem for 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.

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems

Citations:

Zbl 0887.35112
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