2013
DOI: 10.18514/mmn.2013.595
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Abstract: We show the existence of the unique solution of impulsive differential equation x 0 .t / D a .t / .x .t / x .bt 1c// C f .t / ; t ¤ n 2 Z C D f1; 2; : : :g ; t 0; x .t / D c t x .t / C d t ; t D n 2 Z C ; with the initial conditions x. 1/ D x 1 ; x .0/ D x 0 ; where b:c denotes the floor integer function. Moreover, we obtain sufficient conditions for the asymptotic constancy of this equation and we compute, as t ! 1, the limits of the solutions of the impulsive equation with c n D 0 in terms of the initial con… Show more

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Cited by 6 publications
(24 citation statements)
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References 22 publications
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“…There still exist interesting problems on Nicholson's model. In [19], [20] there is a detailed analysis for impulsive di¤erential equations with piecewise constant arguments. Nicholson's blow ‡ies model can be considered with piecewise constant arguments and the asymptotic constancy of the positive solutions may be studied.…”
Section: Discussionmentioning
confidence: 99%
“…There still exist interesting problems on Nicholson's model. In [19], [20] there is a detailed analysis for impulsive di¤erential equations with piecewise constant arguments. Nicholson's blow ‡ies model can be considered with piecewise constant arguments and the asymptotic constancy of the positive solutions may be studied.…”
Section: Discussionmentioning
confidence: 99%
“…On the other hand, it is well known that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics do exist impulsive effects [10]. Recently, the existence, uniqueness and oscillation of the exact solutions of impulsive differential equations with piecewise constant arguments have been widely studied [3,4,[8][9][10]. But many impulsive differential equations with piecewise constant arguments can not be solved exactly or the solving is complicated.…”
Section: Introductionmentioning
confidence: 99%