zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Oscillation of higher order impulsive differential equations of mixed type with constant argument at fixed time. (English) Zbl 1156.34318
Summary: This paper studies the oscillation of a kind of impulsive differential equation of mixed type with piecewise constant argument, and some oscillation criteria about this kind of impulsive differential equation are obtained. The effect of initial value problems upon the oscillation of solutions is stressed. Finally examples are given to illustrate our results.
MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A37Differential equations with impulses
References:
[1]Simeonov, P. S.; Bainov, D. D.: On the asymptotic equivalence of systems with impulse effect, J. math. Anal. appl. 135, 591-610 (1982) · Zbl 0671.34051 · doi:10.1016/0022-247X(88)90174-6
[2]Fu, Xilin; Yan, Baoqiang; Liu, Yansheng: Introduction of impulsive differential systems, (2005)
[3]Xinli Dai, Some results for impulsive differential systems, Master’s degree thesis, Shandong Normal University, 2005
[4]Mcrae, Farzana A.: Practical stability of impulsive control systems, J. math. Anal. appl. 181, 656-672 (1994) · Zbl 0860.93024 · doi:10.1006/jmaa.1994.1050
[5]Akinyele, Olusola: Cone-valued Lyapunov functions and stability of impulsive control systems, Nonlinear anal. 39, 247-259 (2000) · Zbl 0939.34057 · doi:10.1016/S0362-546X(98)00160-6
[6]Lakshmikantham, V.; Bainov, D. D.; Simecnov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[7]Banov, D. D.; Dumitrova, M. B.: Oscillation of the bounded solutions of impulsive differential-difference equations of second order, Appl. math. Comput. 114, 61-68 (2000) · Zbl 1030.34062 · doi:10.1016/S0096-3003(99)00102-2
[8]Chen, Y.; Feng, W.: Oscillations of second order nonlinear ODE with impulsives, J. math. Anal. appl. 210, 667-678 (1997) · Zbl 0877.34014 · doi:10.1006/jmaa.1997.5378
[9]Feng, W.; Chen, Y.: Oscillation of a second order FDE with impulsive, Dynam. contin. Discrete impulsive (Ser. A) 9, 367-376 (2002)
[10]Feng, W.: Oscillations of fourth order ODE with impulsives, Ann. differential equations 19, No. 2, 136-145 (2003) · Zbl 1065.34026
[11]Banov, D. D.; Dumitrova, M. B.: Oscillation of the bounded solutions of impulsive differential-difference equations of second order, Appl. math. Comput. 114, 61-68 (2000) · Zbl 1030.34062 · doi:10.1016/S0096-3003(99)00102-2
[12]Li, X.; Weng, P.: Impulsive stabilization of a kind of nonlinear differential equation, Appl. math. J.C. univ. Ser. A 18, No. 4, 408-416 (2003) · Zbl 1050.34087
[13]Luo, M.: The oscillation and stability of impulsive differential equations of mixed type with constant argument, J. Hefei univ. 14, No. 3, 8-10 (2004)
[14]Wen, L.; Chen, Y.: Razumikhin type theorems for functional differential equations with impulse, Dynam. contin. Discrete impulsive syst. 6, 389-400 (1999) · Zbl 0936.34070