2013
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…
Help me understand this reportSearch citation statements
Paper Sections
Select...
1
1
Citation Types
0
2
0
Year Published
2015
2019
Publication Types
Select...
2
Relationship
0
2
Authors
Journals
Cited by 6 publications
(24 citation statements)
References 22 publications
(24 reference statements)
0
2
0
“…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%
scite is a Brooklyn-based startup that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.