## Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics.(English)Zbl 1022.34070

The authors consider the following system of functional-differential equations $\dot{x}(t)=f(t,x_t),\quad t>t_0,\;t\neq t_k;\qquad x(t_k+0)-x(t_k-0)=I_k(x(t_k-0)),\quad t_k>t_0.$ They obtain sufficient conditions for stability, uniform stability and asymptotic stability. As an application they investigate an impulsive delay logistic equation. Stability conditions obtained for this equation are not explicit.

### MSC:

 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general) 34K45 Functional-differential equations with impulses
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### References:

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