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B.F. Bylov, R.E. Vinograd, D.M. Grobman, V.V. Nemytskii (1966)
Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti
ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 2, pp. 208–217. c Pleiades Publishing, Ltd., 2007. Original Russian Text c N.V. Kozhurenko, E.K. Makarov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 2, pp. 203–211. ORDINARY DIFFERENTIAL EQUATIONS On Sufficient Conditions for the Applicability of an Algorithm for the Computation of the Sigma-Exponent to Integrally Bounded Perturbations N. V. Kozhurenko and E. K. Makarov Institute of Mathematics, National Academy of Sciences, Minsk, Belarus Received September 20, 2005 DOI: 10.1134/S0012266107020085 Consider the linear differential system x ˙ = A(t)x, x ∈ R,t ≥ 0, (1) with piecewise continuous bounded coefficient matrix A such that A(t)≤ M< +∞ for all t ≥ 0. Along with (1), consider the perturbed system y˙ = A(t)y + Q(t)y, y ∈ R,t ≥ 0, (2) with piecewise continuous perturbation matrix Q satisfying the integral boundedness condition t+1 [1, p. 252], that is, the inequality Q(τ )dτ ≤ C < +∞ for all t ≥ 0, where C is a constant Q Q depending on Q.By X(t, τ ) we denote the Cauchy matrix of system (1), and by λ (A + Q)we denote the higher exponent of system (2). Let M be
Differential Equations – Springer Journals
Published: Mar 20, 2007
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