CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER#br#
CURVES

doi:10.1016/S0252-9602(12)60077-0

摘要/Abstract

摘要：

The basic objects of investigation in this article are nonlinear impulsive dif-ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf-ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.

关键词: Impulsive differential equations, initial condition, barrier curves, continuous dependence, population dynamics

Abstract:

Key words: Impulsive differential equations, initial condition, barrier curves, continuous dependence, population dynamics

中图分类号:

34A37

K.G. Dishlieva. CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER#br# CURVES[J]. 数学物理学报(英文版), 2012, 32(3): 1035-1052.

K.G. Dishlieva. CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER[J]. Acta mathematica scientia,Series B, 2012, 32(3): 1035-1052.

参考文献

[1] 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 Model Numer Anal, 1990, 24(6): 681–692

[2] Benchohra M, Henderson J, Ntouyas S. Impulsive differential equations and inclusions. Hindawi Publishing Corporations, 2006, 2

[3] Benchohra M, Henderson J, Ntouyas S. Impulsive neutral functional differential equations in Banach spaces. Applicable Analysis, 2001, 80(3): 353–365

[4] Benchohra M, Henderson J, Ntouyas S, Ouahab A. Impulsive functional differential equations with variable times. Computers & Math with Applications, 2004, 47: 1659–1665

[5] Benchohra M, Ouahab A. Impulsive neutral functional differential equations with variable times. Nonlinear Analysis: Theory, Methods & Applications, 2003, 55: 679–693

[6] Coddington E, Levinson N. Theory of ordinary differential equations. New York, Toronto, London: McGraw-Hill Book Company, 1955

[7] Dishliev A, Bainov D. Dependence upon initial conditions and parameters of solutions of impulsive differ-ential equations with variable structure. Int J Theor Phys, 1990, 22(2): 519–539

[8] Dong L, Chen L, Sun L. Optimal harvesting policies for periodic Gompertz systems. Nonlinear Anal RWA, 2007, 8: 572–578

[9] Frigon M, O'Regan D. Impulsive differential equations with variable times, Nonlinear Analysis: Theory, Methods & Applications, 1996, 26: 1913–1922

[10] Frigon M, O'Regan D. First order impulsive initial and periodic problems with variable moments. J Math Anal Appl, 1999, 233: 730–739

[11] Frigon M, O'Regan D. Second order Sturm-Liouville BVP's with impulses at variable moments. Dynam Contin. Discrete Impuls. Systems, 2001, 8(2): 149–159

[12] Lakshmikantham V, Bainov D, Simeonov P. Theory of impulsive differential equations. Singapore, New Jersey, London, Hong Kong: World Scientific, 1989

[13] Liu X. Stability results for impulsive differential systems with application to population growth models. Dyn Stabil Syst, 1994, 9(2): 163–174

[14] 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 of Mathematical Chemistry, 2010, 47: 123–144

[15] Milman V, Myshkis A. On stability of motion in the presence of impulses. Sibirskii Math J, 1960, 1(11): 233–237 (in Russian)

[16] 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, 2009, 224: 544–555

[17] 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, 2009, 98: 67–72

[18] Nieto J, O’Regan D. Variational approach to impulsive differential equations. Nonlinear Analysis: Real World Applications, 2009, 10: 680–690

[19] Nieto J, Rodriges-Lopez R. Boundary value problems for a class of impulsive functional equations. Com-puters & Math with Applications, 2008, 55(12): 2715–2731

[20] Samojlenko A, Perestyuk N. Impulsive differential equations. Singapore, New Jersey, London, Hong Kong: World Scientific, 1995

[21] Stamov G, Stamova I. Almost periodic solutions for impulsive neural networks with delay. Applied Math Model, 2007, 31: 1263–1270

[22] Stamova I. Stability analysis of impulsive functional differential equations. Berlin, New York: Walter de Gruyter, 2009

[23] Stamova I, Emmenegger G F. Stability of the solutions of impulsive functional differential equations mod-eling price fluctuations in single commodity markets. Int J of Applied Math, 2004, 15(3): 271–290

[24] Stamova I, Stamov G. Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics. J of Computational and Applied Math, 2001, 130: 163–171

[25] 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. Hindawi Publishing Corporations, Boundary Value Problems, 2008, 2008, Article ID 197205

[26] Yan J, Zhao A, Nieto J. Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems. Math and Computer Model, 2004, 40(5/6): 509–518

[27] Zavalishchin S, Sesekin A. Dynamic impulse systems. Theory and applications. Mathematics and its applications. Dordrecht: Kluwer Academic Publishers, 1997

[28] Zeng G, Wang F, Nieto J. Complexity of a delayed predator-prey model with impulsive harvest and Holling-type II functional response. Advances in Complex Systems, 2008, 11: 77–97

[29] Zhang H, Chen L, Nieto J. A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear Analysis: Real World Applications, 2008, 9: 1714–1726

[30] Zhang X, Shuai Z, Wang K. Optimal impulsive harvesting policy for single population. Nonlinear Analysis: Real World Applications, 2008, 9: 1714–1726

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER#br# CURVES

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

Metrics

本文评价

推荐阅读 10

[1]	郭柏灵, 席肖玉. GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS[J]. 数学物理学报(英文版), 2017, 37(3): 573-583.
[2]	马和平, 刘斌. EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY[J]. 数学物理学报(英文版), 2017, 37(1): 235-258.
[3]	谭连生. ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2000, 20(2): 261-272.