Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 62, pp. 1–17. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu PSEUDO ALMOST PERIODIC SOLUTIONS FOR A LASOTA-WAZEWSKA MODEL SAMIRA RIHANI, AMOR KESSAB, FAROUK CH ´ ERIF Abstract. In this work, we consider a new model describing the survival of red blood cells in animals. Specifically, we study a class of Lasota-Wazewska equation with pseudo almost periodic varying environment and mixed delays. By using the Banach fixed point theorem and some inequality analysis, we find sufficient conditions for the existence, uniqueness and stability of solutions. We generalize some results known for one type of delay and for the Lasota- Wazewska model with almost periodic and periodic coefficients. An example illustrates the proposed model. 1. Introduction In 1976 Wazewska and Lasota [26] proposed the delay logistic equation with one constant concentrated delay N ′ (t)= −µN (t)+ pe −rN(t−τ ) to describe the survival of red blood cells in an animal, where N (t) denotes the number of red blood cells at time t, µ is the probability of death of a red blood cell p and r are positive constants related to the production of red blood cells per unit time and τ is the time required to produce a red blood cell. See also [16, 17]. Under some additional assumptions, Gopalsamy and Trofimchuk [13] obtained that the Lasota-Wazewska model with one discrete delay x ′ (t)= −α(t)x(t)+ β(t)e −νx(t−τ ) has a globally attractive almost periodic solution. In [23], the existence the oscil- lations and the global attractivity of the unique positive periodic solution of the following equation x ′ (t)= −α(t)x(t)+ β(t)e −ax(t−nT ) were discussed. In particular, by applying Mawhin’s continuation theorem of co- incidence degree [12] several sufficient conditions were given ensuring the existence of the periodic solution. Here a> 0,α(·),β(·) are positive periodic functions of a fixed period T and n is a positive integer. The authors investigated several results regarding the oscillations and the global attractivity of existence of the periodic solution. Besides, in the work [15] by Huang et al the following delay differential 2010 Mathematics Subject Classification. 35B15, 47H10, 93A30. Key words and phrases. Lasota-Wazewska equation; pseudo almost periodic; mixed delays. c 2016 Texas State University. Submitted December 7, 2015. Published March 4, 2016. 1