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)
Asymptotic behavior of solutions of differential equations with piecewise constant arguments. (English) Zbl 1152.34348
Summary: The main goal of the work is to obtain sufficient conditions for the asymptotic equivalence of a linear system of ordinary differential equations and a quasilinear system of differential equations with piecewise constant argument.

34D05Asymptotic stability of ODE
34C41Equivalence, asymptotic equivalence
Full Text: DOI
[1] Akhmet, M. U.: Integral manifolds of differential equations with piecewise constant argument of generalized type. Nonlinear anal. 66, 367-383 (2007) · Zbl 1122.34054
[2] Akhmet, M. U.; Tleubergenova, M.: On asymptotic equivalence of impulsive linear homogeneous differential systems. Math. J. 2, 15-18 (2002) · Zbl 1132.34303
[3] Akhmet, M. U.; Tleubergenova, M.; Zafer, A.: Asymptotic equivalence of differential equations and asymptotically almost periodic solutions. Nonlinear anal. TMA 67, 1870-1877 (2007) · Zbl 1189.34084
[4] Busenberg, S.; Cooke, K. L.: Models of vertically transmitted diseases with sequential--continuous dynamics. Nonlinear phenomena in mathematical sciences, 179-187 (1982) · Zbl 0512.92018
[5] Cooke, K. L.; Wiener, J.: Retarded differential equations with piecewise constant delays. J. math. Anal. appl. 99, 265-297 (1984) · Zbl 0557.34059
[6] Li, X.; Wang, Z.: Global attractivity for a logistic equation with piecewise constant arguments. Fields inst. Commmun 42, 215-222 (2004) · Zbl 1068.34075
[7] Marconato, S. A. S.: The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps. Dyn. contin. Discrete impuls. Syst. ser. A math. Anal. 12, 755-768 (2005) · Zbl 1093.34039
[8] Muroya, Y.; Kato, Y.: On gopalsamy and Liu’s conjecture for global stability in a population model. J. comput. Appl. math. 181, 70-82 (2005) · Zbl 1065.92034
[9] Nemytskii, V. V.; Stepanov, V. V.: Qualitative theory of differential equations. (1966) · Zbl 0089.29502
[10] Wiener, J.: Generalized solutions of functional differential equations. (1993) · Zbl 0874.34054
[11] Yakubovich, V. A.: On the asymptotic behavior of systems of differential equations. Mat. sbornik 28, 217-240 (1951)