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Positive almost periodic solution for a class of Lasota-Wazewska model with infinite delays. (English) Zbl 1277.34104
Summary: By using a fixed theorem in cones, we study the existence of a unique positive almost periodic solution for a generalized Lasota-Wazewska model with infinite delays. Some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived, and it cannot be obtained by the contraction mapping principle. Furthermore, under proper conditions, we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.

##### MSC:
 34K14 Almost and pseudo-periodic solutions of functional differential equations 34K60 Qualitative investigation and simulation of models 34K25 Asymptotic theory of functional-differential equations 34K20 Stability theory of functional-differential equations
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##### References:
 [1] Alzabut, J. O.; Stamov, G. T.; Sermutlu, E.: Positive almost periodic solutions for a delay logarithmic population model, Math. comput. Model. 53, 161-167 (2011) · Zbl 1211.34084 · doi:10.1016/j.mcm.2010.07.029 [2] He, M. X.; Chen, F. D.; Li, Z.: Almost periodic solution of an impulse differential equation model of plankton allelopathy, Nonlinear anal. 11, 2296-2301 (2010) · Zbl 1200.34050 · doi:10.1016/j.nonrwa.2009.07.004 [3] Li, Z.; Chen, F.: Almost periodic solutions of a discrete almost periodic logistic equation, Math. comput. Model. 50, 254-259 (2009) · Zbl 1185.39011 · doi:10.1016/j.mcm.2008.12.017 [4] Wang, Y. H.; Xia, Y. H.: The existence of almost periodic solutions of a certain nonlinear system, Commun. nonlinear sci. Numer. simulat. 16, 106. 0-107 (2011) · Zbl 1221.34118 · doi:10.1016/j.cnsns.2010.05.003 [5] Abbas, S.; Bahuguna, D.: Almost periodic solutions of neutral functional differential equations, Comput. math. Appl. 55, No. 11, 2539-2601 (2008) · Zbl 1142.34367 · doi:10.1016/j.camwa.2007.10.011 [6] Chen, X. X.; Lin, F. X.: Almost periodic solutions of neutral differential equations, Nonlinear anal. 11, 1182-1189 (2010) · Zbl 1191.34089 · doi:10.1016/j.nonrwa.2009.02.010 [7] He, C. Y.: Almost periodic differential equations, (1992) [8] Fink, A. M.: Almost periodic differential equations, Lect. notes math. 377 (1974) · Zbl 0325.34039 [9] Gopalsamy, K.; Trofimchuk, S.: Almost periodic solutions of lasota -- wazewska-type delay differential equation, J. math. Anal. appl. 237, 106-127 (1999) · Zbl 0936.34058 · doi:10.1006/jmaa.1999.6466 [10] Wazewska-Czyzewska, M.; Lasota, A.: Mathematical problems of the dynamics if red blood cells system, Ann. Polish math. Soc. ser. III appl. Math. 17, 23-40 (1988) [11] Huang, Z. D.; Gong, S. H.; Wang, L. J.: Positive almost periodic solution for a class of lasota -- wazewska model with multiple timing-varing delays, Comput. math. Appl. 61, 755-760 (2011) · Zbl 1217.34114 · doi:10.1016/j.camwa.2010.12.019 [12] D.J. Guo, Nonlinear Functional Analysis Shandond Science and Technology Press, Jinan 2001 (in Chinese). [13] Liu, G.; Zhao, A.; Yan, J.: Existence and global at activity of unique positive periodoic solution for a lasota -- wazewska model, Nonlinear anal. 64, 1737-1746 (2006) · Zbl 1099.34064 · doi:10.1016/j.na.2005.07.022