×

Existence of positive periodic solutions for neutral multi-delay logarithmic population model. (English) Zbl 1303.92101

Summary: A new result is obtained for the existence of positive periodic solutions to a neutral multi-delay logarithmic population model. Our analysis mainly relies on an abstract continuous theorem of \(k\)-set contractive operator. We also give an example to illustrate the applicability of our results.

MSC:

92D25 Population dynamics (general)
34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0559.47040
[2] Gopalsamy, K.; He, X.; Wen, L., On a periodic neutral logistic equation, Glasgow Math. J., 33, 281-286 (1991) · Zbl 0737.34050
[3] Gaines, R. E.; Mawhin, J. L., Coninsidence degree and nonlinear differential equation, Lecture notes in Math, vol. 568 (1997), Springer-Verlag
[4] Kirlinger, G., Permanence in Lotka-Volterra equation, linked prey-predator system, Math. Biosci., 82, 165-191 (1986) · Zbl 0607.92022
[5] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press: Academic Press New York · Zbl 0777.34002
[6] Kuang, Y.; Feldstein, A., Boundedness of a nonlinear nonautonomous neutral delay equation, J. Math. Anal. Appl., 156, 293-304 (1991) · Zbl 0731.34089
[7] Lu, S. P.; Ge, W. G., Existence of positive periodic solutions for neutral logarithmic population model with multiple delays, J. Comput. Appl. Math., 166, 2, 371-383 (2004) · Zbl 1061.34053
[8] 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
[9] Petryshyn, W. V.; Yu, Z. S., Existence theorems for higher order nonlinear periodic boundary value problems, Nonlinear Anal., 9, 943-969 (1982) · Zbl 0525.34015
[10] Pielou, E. C., Mathematics Ecology (1977), Wiley: Wiley New York · Zbl 0259.92001
[11] Yang, Z.; Cao, J., Sufficient conditions for the existence of positive periodic solutions of a class of neutral delay model, Appl. Math. Comput., 142, 123-142 (2003) · Zbl 1037.34066
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.