# zbMATH — the first resource for mathematics

Positive almost periodic solutions for a delay logarithmic population model. (English) Zbl 1211.34084
Summary: By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.

##### MSC:
 34K14 Almost and pseudo-almost periodic solutions to functional-differential equations 92D30 Epidemiology
Full Text:
##### References:
 [1] Cushing, J.M., Integrodifferential equations and delay models in population dynamics: lecture notes in biomathematics, vol. 20, (1977), Springer-Verlag Berlin · Zbl 0363.92014 [2] Edelstein-Kashet, L., Mathematical models in biology, (1988), Random House New York [3] Kot, M., Elements of mathematical ecology, (2001), Camb. Univ. Press [4] Brauer, F.; Castilli-Chavez, C., Mathematical models in population biology and epidemiology, (2001), Springer Berlin · Zbl 0967.92015 [5] Gopalsamy, K., Stability and oscillation in delay differential equations of population dynamics, (1992), Kluwer Academic Publisher Boston · Zbl 0752.34039 [6] Kirlinger, G., Permanence in lotka – voltera equations: linked prey – predator systems, Math. biosci., 82, 165-191, (1986) · Zbl 0607.92022 [7] Chen, F., Periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model, Appl. math. comput., 171, 760-770, (2005) · Zbl 1089.92038 [8] Wang, C.; Shi, J., Periodic solution for a delay multispecies logarithmic population model with feedback control, Appl. math. comput., 193, 257-265, (2007) · Zbl 1193.34144 [9] Wang, Q.; Dai, B., Existence of positive periodic solutions for neutral population model with delays and impulse, Nonlinear anal., 69, 3919-3930, (2008) · Zbl 1166.34047 [10] Zhao, W., New results of existence and stability of periodic solution for a delay multispecies logarithmic population model, Nonlinear anal.: real world appl., 10, 544-553, (2009) · Zbl 1154.34366 [11] Wang, Q.; Wang, Y.; Dai, B., Existence and uniqueness of positive periodic solutions for a neutral logarithmic population model, Appl. math. comput., 213, 1, 137-147, (2009) · Zbl 1177.34093 [12] Alzabut, J.O.; Abdeljawad, T., Existence and global attractivity of impulsive delay logarithmic model of population dynamics, Appl. math. comput., 198, 1, 463-469, (2008) · Zbl 1163.92033 [13] Ahmad, S.; Stamov, G.Tr., Almost periodic solutions of $$n$$-dimensional impulsive competitive systems, Nonlinear anal.: real world appl., 10, 3, 1846-1853, (2009) · Zbl 1162.34349 [14] Ahmad, S.; Stamov, G.Tr., On almost periodic processes in impulsive competitive systems with delay and impulsive perturbations, Nonlinear anal.: real world appl., 10, 2857-2863, (2009) · Zbl 1170.45004 [15] Li, Z.; Chen, F., Almost periodic solutions of a discrete almost periodic logistic equation, Math. comput. modelling, 50, 254-259, (2009) · Zbl 1185.39011 [16] Luo, B., Travelling waves of a curvature flow in almost periodic media, J. differential equations, 247, 2189-2208, (2009) · Zbl 1182.35073 [17] Alzabut, J.O.; Nieto, J.J.; Stamov, G.Tr., Existence and exponential stability of positive almost periodic solutions for a model of hematpoiesis, Bound. value probl., 2009, (2009), Article ID 127510 · Zbl 1186.34116 [18] Yuan, R., On almost periodic solutions of logistic delay differential equations with almost periodic time dependence, J. math. anal. appl., 330, 780-798, (2007) · Zbl 1125.34055 [19] Wu, W.; Ye, Y., Existence and stability of almost periodic solutions of nonautonomous competitive systems with weak allee effect and delays, Commun. nonlinear sci. numer. simul., 14, 11, 3993-4002, (2009) · Zbl 1221.34185 [20] Stamov, G.T.; Petrov, N., Lyapunov – razumikhin method for existence of almost periodic solutions of impulsive differential – difference equations, Nonlinear stud., 15, 2, 151-163, (2008) · Zbl 1156.34057 [21] Stamov, G.T.; Stamova, I.M., Almost periodic solutions for impulsive neutral networks with delay, Appl. math. model., 31, 1263-1270, (2007) · Zbl 1136.34332 [22] Wang, Q.; Zhang, H.; Wang, Y., Existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model, Nonlinear anal., 72, 12, 4384-4389, (2010) · Zbl 1194.34153 [23] Besicovitch, A.S., Almost periodic functions, (1954), Dover Publications New York · Zbl 0065.07102 [24] Fink, A., Almost periodic differential equations: lecture notes in mathematics, vol. 377, (1974), Springer Berlin [25] Alzabut, J.O.; Stamov, G.Tr.; Sermutlu, E., On almost periodic solutions for an impulsive delay logarithmic population model, Math. comput. modelling, 51, 625-631, (2010) · Zbl 1190.34087 [26] Mawhin, J., Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces, J. differential equations, 12, 610-636, (1972) · Zbl 0244.47049 [27] Gaines, R.E.; Mawhin, J.L., Coincidence degree and nonlinear differential equations, (1977), Springer Berlin · Zbl 0326.34021
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.