# 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)
Existence of positive periodic solutions for a class of difference equations with several deviating arguments. (English) Zbl 1052.39008
The authors consider the general periodic logistic difference equation $$\triangle x(t) = x(t)[a(t)-g(t,x(t-\tau_1(t)),\ldots,x(t-\tau_n(t)))]$$ where $t\in Z$ and $a$, $g(\cdot,x_1,\ldots,x_n)$, $\tau_i(\cdot)$ are $T$-periodic. Conditions are given for the existence of a positive $T$-periodic solution of the equation, using a continuation theorem from {\it R. E. Gaines} and {\it J. L. Mawhin} [Coincidence degree, and nonlinear differential equations (1977; Zbl 0339.47031)].

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis
Full Text:
##### References:
 [1] Jiang, D. Q.; Wei, J. J.: Existence of positive periodic solution for nonautonomous delay differential equations. Chin. ann. Of math. (Series A) 20A, 716-720 (1999) [2] Li, Y. K.: Existence and global attractivity of positive periodic solution for a class of delay differential equations. Science in China (Series A) 28, 108-118 (1998) [3] Gopalsamy, K.: Stability and oscillations in delay differential equations of population dynamics. (1992) · Zbl 0752.34039 [4] Pielou, E. C.: Mathematics ecology. (1977) · Zbl 0259.92001 [5] Lenhart, S.; Travis, C.: Global stability of a biological model with time delay. Proc. amer. Math. soc. 96, 75-78 (1986) · Zbl 0602.34044 [6] Kelley, W. G.; Peterson, A. C.: Difference equations: an introduction with applications. (1991) · Zbl 0733.39001 [7] Zhang, R. Y.; Wang, Z. C.; Cheng, Y.; Wu, J.: Periodic solutions of a single species discrete population model with periodic harvest/stock. Computers math. Applic. 39, No. 1/2, 77-90 (2000) · Zbl 0970.92019 [8] Gopalsamy, K.; Lalli, B. S.: Oscillatory and asymptotic behavior of a multiplicative delay logistic equation. Dynamics and stability of system 7, 35-42 (1992) · Zbl 0764.34049 [9] Mallet-Paret, J.; Nussbaum, R.: Global continuation and asymptotic behavior for periodic solutions of a differential-delay equation. Ann. di. Math. pured. Appl. 145, 33-128 (1986) · Zbl 0617.34071 [10] Kuang, Y.: Global stability for a class of nonlinear nonautonomous delay logistic equations. Nonlinear analysis 17, 627-634 (1991) · Zbl 0766.34053 [11] Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations. (1977) · Zbl 0339.47031