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)
Unique existence theorem of solution of almost periodic differential equations on time scales. (English) Zbl 1239.34109
Summary: By using the theory of calculus on time scales and the $M$-matrix theory, the existence theorem of a solution for almost periodic differential equations on almost periodic time scales is established.

34N05Dynamic equations on time scales or measure chains
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
Full Text: DOI
[1] Y. Hamaya, “Existence of an almost periodic solution in a difference equation with infinite delay,” Journal of Difference Equations and Applications, vol. 9, no. 2, pp. 227-237, 2003. · Zbl 1033.39009 · doi:10.1080/1023619021000035836
[2] Y. Song and H. Tian, “Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay,” Journal of Computational and Applied Mathematics, vol. 205, no. 2, pp. 859-870, 2007. · Zbl 1122.39007 · doi:10.1016/j.cam.2005.12.042
[3] Y. Xia, J. Cao, and M. Lin, “New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays,” Chaos, Solitons and Fractals, vol. 31, no. 4, pp. 928-936, 2007. · Zbl 1137.68052 · doi:10.1016/j.chaos.2005.10.043
[4] E. H. Dads, P. Cieutat, and K. Ezzinbi, “The existence of pseudo-almost periodic solutions for some nonlinear differential equations in Banach spaces,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 4, pp. 1325-1342, 2008. · Zbl 1151.34035 · doi:10.1016/j.na.2007.06.037
[5] N. Boukli-Hacene and K. Ezzinbi, “Weighted pseudo almost periodic solutions for some partial functional differential equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 9, pp. 3612-3621, 2009. · Zbl 1175.34101 · doi:10.1016/j.na.2009.02.022
[6] M. Bohner and A. Peterson, Dynamic Equations on Time Scales. An Introduction with Applications, Birkhauser Boston, Boston, Mass, USA, 2001. · Zbl 0978.39001
[7] S. Hilger, “Analysis on measure chains-a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18-56, 1990. · Zbl 0722.39001 · doi:10.1007/BF03323153
[8] Y. Li and C. Wang, “Almost periodic functions on time scales and applications,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 727068, 20 pages, 2011. · Zbl 1232.26055 · doi:10.1155/2011/727068
[9] R. C. McKellar and K. Knight, “A combined discrete-continuous model describing the lag phase of Listeria monocytogenes,” International Journal of Food Microbiology, vol. 54, no. 3, pp. 171-180, 2000. · doi:10.1016/S0168-1605(99)00204-4
[10] C. C. Tisdell and A. Zaidi, “Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 11, pp. 3504-3524, 2008. · Zbl 1151.34005 · doi:10.1016/j.na.2007.03.043
[11] M. Fazly and M. Hesaaraki, “Periodic solutions for predator-prey systems with Beddington-DeAngelis functional response on time scales,” Nonlinear Analysis. Real World Applications, vol. 9, no. 3, pp. 1224-1235, 2008. · Zbl 1145.92035 · doi:10.1016/j.nonrwa.2007.02.012
[12] Y. Li and M. Hu, “Three positive periodic solutions for a class of higher-dimensional functional differential equations with impulses on time scales,” Advances in Difference Equations, vol. 2009, Article ID 698463, 18 pages, 2009. · Zbl 1213.34117 · doi:10.1155/2009/698463