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Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects. (English) Zbl 1084.34071
Existence and global attractivity of positive periodic solutions are studied for the following nonlinear delay equation with impulses $$\dot{y}(t)=-a(t)y(t)+g(t, y(t-\tau(t)),\quad t\neq t_j\ y(t_j^{+})=y(t_j^-)+I_j(y(t_j)).$$ As corollaries the authors obtain explicit conditions for many popular equations of mathematical biology: logistic equation, Mackey-Glass equation, blood cell production equation, and Nicholson’s blowflies equation.

34K45Functional-differential equations with impulses
34K13Periodic solutions of functional differential equations
Full Text: DOI
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