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Existence and global attractivity of positive periodic solutions of functional differential equations with impulses. (English) Zbl 1061.34059

Existence and global attractivity of positive periodic solutions are obtained for the following nonlinear delay differential equation with impulses

y ˙(t)=y(t)F(t,y(t-τ 1 (t)),,y(t-τ n (t))),y(t k + )=b k y(t k ),k=1,2·

Applications to logistic equations with several delays are presented. For the proof the authors apply coincidence degree theory and the method of Lyapunov functionals.

MSC:
34K45Functional-differential equations with impulses
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models