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 and uniqueness of positive periodic solutions for a neutral logarithmic population model. (English) Zbl 1177.34093
The authors obtain criteria for the existence, global attractivity of positive periodic solution of a neutral delay logarithmic population model with multiple delays by using the theory of k-set contractive operators. An example is provided to illustrate the result.
MSC:
34K13Periodic solutions of functional differential equations
47N20Applications of operator theory to differential and integral equations
34K40Neutral functional-differential equations
References:
[1]Gopalsamy, K.: Stability and oscillation in delay differential equations of population dynamics, Mathematics and its applications 74 (1992) · Zbl 0752.34039
[2]Kirlinger, G.: Permanence in Lotka – Volterra equations linked prey – predator systems, Math. biosci. 82, 165-169 (1986) · Zbl 0607.92022 · doi:10.1016/0025-5564(86)90136-7
[3]Li, Y. K.: Attractivity of a positive periodic solution for all other positive solution in a delay population model, Appl. math. -JCU 12, No. 3, 279-282 (1997) · Zbl 0883.92023
[4]Liu, Z. J.: Positive periodic solutions for delay multispecies logrithmic population model, J. eng. Math. 19, No. 4, 11-16 (2002) · Zbl 1041.34059
[5]Zhou, Y. G.; Tang, X. H.: On existence of periodic solutions of Rayleigh equation of retarded type, J. comput. Appl. math. 203, 1-5 (2007) · Zbl 1115.34067 · doi:10.1016/j.cam.2006.03.002
[6]Fang, H.; Li, J. B.: On the existence of periodic solutions of a neutral delay model of single-species population growth, J. math. Anal. appl. 259, 8-17 (2001) · Zbl 0995.34073 · doi:10.1006/jmaa.2000.7340
[7]Yang, Z. H.; Cao, J. D.: Sufficient conditions for the existence of positive periodic solutions of a class of neutral delays models, Appl. math. Comput. 142, No. 1, 123-142 (2003) · Zbl 1037.34066 · doi:10.1016/S0096-3003(02)00288-6
[8]Yang, Z. H.; Cao, J. D.: Positive periodic solutions of neutral Lotka – Volterra system with periodic delays, Appl. math. Comput. 149, No. 3, 661-687 (2004) · Zbl 1045.92037 · doi:10.1016/S0096-3003(03)00170-X
[9]Li, Y. K.: On a periodic neutral delay Lotka – Volterra system, Nonlinear anal. 39, 767-778 (2000) · Zbl 0943.34058 · doi:10.1016/S0362-546X(98)00235-1
[10]Chen, F. D.; Lin, F. X.; Chen, X. X.: Sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control, Appl. math. Comput. 158, No. 1, 45-68 (2004) · Zbl 1096.93017 · doi:10.1016/j.amc.2003.08.063
[11]Chen, F. D.: Positive periodic solutions of neutral Lotka – Volterra system with feedback control, Appl. math. Comput. 162, No. 3, 1279-1302 (2005) · Zbl 1125.93031 · doi:10.1016/j.amc.2004.03.009
[12]Fang, H.: Positive periodic solutions of n-species neutral delay systems, Czech math. J. 53, No. 3, 561-570 (2003) · Zbl 1080.34530 · doi:10.1023/B:CMAJ.0000024503.03321.b1
[13]Liu, Z. J.: Positive periodic solution for a neutral delay competitive system, J. math. Anal. appl. 293, No. 1, 181-189 (2004) · Zbl 1057.34095 · doi:10.1016/j.jmaa.2003.12.035
[14]Raffoul, Y. N.: Periodic solutions for neutral nonlinear differential equations with functional delay, E.j.d.e. 2003, No. 102, 1-7 (2003) · Zbl 1054.34115 · doi:emis:journals/EJDE/Volumes/2003/102/abstr.html
[15]Gopalsamy, K.: A simple stability criterion for linear neutral differential systems, Funkcial ekvac. 28, 33-38 (1985) · Zbl 0641.34069
[16]Huo, Haifeng: Existence of positive periodic solutions of a neutral delay loka – Volterra systems with impulses, Comput. math. Appl. 48, 1833-1846 (2004) · Zbl 1070.34109 · doi:10.1016/j.camwa.2004.07.009
[17]Xia, Yonhui: Positive periodic solutions for a neutral impulsive delayed Lotka – Volterra competition systems with the effect of toxic substance, Nonlinear anal.: RWA 8, 204-221 (2007) · Zbl 1121.34075 · doi:10.1016/j.nonrwa.2005.07.002
[18]Wang, Qi; Dai, Binxiang: Existence of positive periodic solutions for neutral population model with delays and impulse, Nonlinear anal.: TMA 69, 3919-3930 (2008) · Zbl 1166.34047 · doi:10.1016/j.na.2007.10.033
[19]Chen, F. D.: Periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model, Appl. math. Comput. 171, 760-770 (2005) · Zbl 1089.92038 · doi:10.1016/j.amc.2005.01.085
[20]Li, Y. K.: On a periodic neutral delay logarithmic population model, J. syst. Sci. math. Sci. 19, No. 1, 34-38 (1999) · Zbl 0953.92025
[21]Lu, S. P.; Ge, W. G.: Existence of positive periodic solutions for neutral logarithmic population model with multiple delays, J. comput. Appl. math. 166, No. 2, 371-383 (2004) · Zbl 1061.34053 · doi:10.1016/j.cam.2003.08.033
[22]Chen, F. D.: Periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model, Appl. math. Comput. 176, 431-441 (2006) · Zbl 1089.92039 · doi:10.1016/j.amc.2005.09.032
[23]R.E. Gaines, J.L. Mawhin, in: Lectures Notes in Mathematics, vol. 568, Springer-Verlag, Berlin, 1977.
[24]Liu, Z. D.; Mao, Y. P.: Existence theorem for periodic solutions of higher order nonlinear differential equations, J. math. Anal. appl. 216, 481-490 (1997) · Zbl 0892.34040 · doi:10.1006/jmaa.1997.5669
[25]Lu, S. P.; Ge, W. G.: Existence of positive periodic solutions for neutral population model with multiple delays, Appl. math. Comput. 153, 885-902 (2004) · Zbl 1042.92026 · doi:10.1016/S0096-3003(03)00685-4
[26]Chen, F. D.: The permanence and global attractivity of Lotka – Volterra competition system with feedback controls, Nonlinear anal.: real world appl. 7, 133-143 (2006) · Zbl 1103.34038 · doi:10.1016/j.nonrwa.2005.01.006
[27]Chen, F. D.: Average conditions for permanence and extinction in nonautonomous gilpin – ayala competition model, Nonlinear anal.: real world appl. 7, 895-915 (2006) · Zbl 1119.34038 · doi:10.1016/j.nonrwa.2005.04.007
[28]Chen, F. D.: On a nonlinear nonautonomous predator – prey model with diffusion and distributed delay, J. comput. Appl. math. 180, 33-49 (2005) · Zbl 1061.92058 · doi:10.1016/j.cam.2004.10.001
[29]Wang, Qi; Dai, B.; Chen, Y.: Multiple periodic solutions of an impulsive predator – prey model with Holling IV functional response, Math. comput. Model. (2008)