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ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS
Simeonov, P.S.,Bainov, D.D. Korean Mathematical Society 1994 대한수학회보 Vol.31 No.1
In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.
CRITERIA FOR DICHOTOMY OF LINEAR INPULSIVE DIFFERENTIAL EQUATIONS
P.S.Simeonov,D.D.Bainov 대한수학회 1993 대한수학회지 Vol.30 No.2
Let Z be the set of all intergers. Let S be the set of real or complex numbers, and let T = (ω_-,ω_+) ⊂ R be a real interval which can be bounded or unbounded. Consider the linear impulsive differential equations x^'=A(t)x, t≠τ_k, x^+=A_kx, t=τ_k,