zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Differentiability of solutions of impulsive differential equations with respect to the impulsive perturbations. (English) Zbl 1231.34018
Summary: The nonlinear impulsive differential equations with fixed moments of impulsive perturbation are the main object of investigation in this paper. Sufficient conditions for these types of equations are obtained, under which their solutions are continuously dependent and differentiable with respect to the initial conditions and the impulsive perturbations. The results are applied to a mathematical model of population dynamics.

34A37Differential equations with impulses
Full Text: DOI
[1] Lakshmikantham, V.; Bainov, D.; Simeonov, P.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[2] Li, J.; Nieto, J.: Existence of positive solutions for multipoint boundary value problem on the half-line with impulses, Boundary value problems 2009 (2009) · Zbl 1177.34041
[3] Milman, V.; Myshkis, A.: On stability of motion in the presence of impulses, Sib. math. J. 1, No. 11, 233-237 (1960)
[4] Samojlenko, A.; Perestyuk, N.: Impulsive differential equations, (1995) · Zbl 0837.34003
[5] Benchohra, M.; Henderson, J.; Ntouyas, S.: Impulsive neutral functional differential equations in Banach spaces, Appl. anal. 80, No. 3, 353-365 (2001) · Zbl 1031.34079 · doi:10.1080/00036810108840997
[6] Benchohra, M.; Henderson, J.; Ntouyas, S.; Ouahab, A.: Impulsive functional differential equations with variable times, Comput. math. Appl. 47, 1659-1665 (2004) · Zbl 1070.34108 · doi:10.1016/j.camwa.2004.06.013
[7] Benchohra, M.; Ouahab, A.: Impulsive neutral functional differential equations with variable times, Nonlinear anal. TMA 55, 679-693 (2003) · Zbl 1043.34085 · doi:10.1016/j.na.2003.08.011
[8] Frigon, M.; O’regan, D.: Impulsive differential equations with variable times, Nonlinear anal. TMA 26, 1913-1922 (1996) · Zbl 0863.34015 · doi:10.1016/0362-546X(95)00053-X
[9] Frigon, M.; O’regan, D.: First order impulsive initial and periodic problems with variable moments, J. math. Anal. appl. 233, 730-739 (1999) · Zbl 0930.34016 · doi:10.1006/jmaa.1999.6336
[10] Frigon, M.; O’regan, D.: Second order Sturm--Liouville bvp’s with impulses at variable moments, Dynam. contin. Discrete impuls. Syst. 8, No. 2, 149-159 (2001) · Zbl 0996.34015
[11] Bainov, D.; Dishliev, A.: Population dynamic control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population, Math. modelling numer. Anal. 24, No. 6, 681-692 (1990) · Zbl 0708.92023
[12] Dishliev, A.; Bainov, D.: Dependence upon initial conditions and parameters of solutions of impulsive differential equations with variable structure, Internat. J. Theoret. phys. 22, No. 2, 519-539 (1990)
[13] Meng, X.; Li, Z.; Nieto, J.: Dynamic analysis of michaelis-menten chemostat-type competition models with time delay and pulse in a polluted environment, J. math. Chem. 47, 123-144 (2010) · Zbl 1194.92075 · doi:10.1007/s10910-009-9536-2
[14] Nie, L.; Peng, J.; Teng, Z.; Hu, L.: Existence and stability of periodic solution of a Lotka--Volterra predator--prey model with state dependent impulsive effects, J. comput. Appl. math. 224, 544-555 (2009) · Zbl 1162.34007 · doi:10.1016/j.cam.2008.05.041
[15] Nie, L.; Teng, Z.; Hu, L.; Peng, J.: The dynamics of a Lotka--Volterra predator--prey model with state dependent impulsive harvest for predator, Biosystems 98, 67-72 (2009)
[16] Nieto, J.; O’regan, D.: Variational approach to impulsive differential equations, Nonlinear anal. RWA 10, 680-690 (2009) · Zbl 1167.34318 · doi:10.1016/j.nonrwa.2007.10.022
[17] Nieto, J.; Rodriges-Lopez, R.: Boundary value problems for a class of impulsive functional equations, Comput. math. Appl. 55, No. 12, 2715-2731 (2008) · Zbl 1142.34362 · doi:10.1016/j.camwa.2007.10.019
[18] Stamov, G.; Stamova, I.: Almost periodic solutions for impulsive neural networks with delay, Appl. math. Model. 31, 1263-1270 (2007) · Zbl 1136.34332 · doi:10.1016/j.apm.2006.04.008
[19] Stamova, I.; Emmenegger, G. -F.: Stability of the solutions of impulsive functional differential equations modeling price fluctuations in single commodity markets, Int. J. Appl. math. 15, No. 3, 271-290 (2004) · Zbl 1067.34084
[20] Stamova, I.; Stamov, G.: Lyapunov-razumikhin method for impulsive functional differential equations and applications to the population dynamics, J. comput. Appl. math. 130, 163-171 (2001) · Zbl 1022.34070 · doi:10.1016/S0377-0427(99)00385-4
[21] Xian, X.; O’regan, D.; Agarwal, R.: Multiplicity results via topological degree for impulsive boundary value problems under non-well-ordered upper and lower solution conditions, Boundary value problems 2008 (2008) · Zbl 1158.34015 · doi:10.1155/2008/197205
[22] Yan, J.; Zhao, A.; Nieto, J.: Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka--Volterra systems, Math. comput. Model. 40, No. 5--6, 509-518 (2004) · Zbl 1112.34052 · doi:10.1016/j.mcm.2003.12.011
[23] Zeng, G.; Wang, F.; Nieto, J.: Complexity of a delayed predator--prey model with impulsive harvest and Holling-type II functional response, Adv. complex syst. 11, 77-97 (2008) · Zbl 1168.34052 · doi:10.1142/S0219525908001519
[24] Zhang, H.; Chen, L.; Nieto, J.: A delayed epidemic model with stage-structure and pulses for pest management strategy, Nonlinear anal. RWA 9, 1714-1726 (2008) · Zbl 1154.34394 · doi:10.1016/j.nonrwa.2007.05.004
[25] Zhang, X.; Shuai, Z.; Wang, K.: Optimal impulsive harvesting policy for single population, Nonlinear anal. RWA 9, 1714-1726 (2008)
[26] Benchohra, M.; Henderson, J.; Ntouyas, S.: Impulsive differential equations and inclusions, Impulsive differential equations and inclusions 2 (2006) · Zbl 1130.34003
[27] Stamova, I.: Stability analysis of impulsive functional differential equations, (2009) · Zbl 1189.34001
[28] Zavalishchin, S.; Sesekin, A.: Dynamic impulse systems. Theory and applications. Mathematics and its applications, (1997) · Zbl 0880.46031
[29] Hartman, F.: Ordinary differential equations, (1964) · Zbl 0125.32102