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Existence and multiplicity of periodic solutions for a generalized hematopoiesis model. (English) Zbl 1378.34094

Summary: A generalization of the nonautonomous Mackey-Glass equation for the regulation of the hematopoiesis with several non-constant delays is studied. Using topological degree methods we prove, under appropriate conditions, the existence of multiple positive periodic solutions. Moreover, we show that the conditions are necessary, in the sense that if some sort of complementary conditions are assumed then the trivial equilibrium is a global attractor for the positive solutions and hence periodic solutions do not exist.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K13 Periodic solutions to functional-differential equations
37C60 Nonautonomous smooth dynamical systems
47N20 Applications of operator theory to differential and integral equations
92C37 Cell biology
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