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Boundedness for impulsive delay differential equations and applications to population growth models. (English) Zbl 1037.34061

Here, the authors apply Lyapunov functions and Razumikhin techniques for the boundedness of the following impulsive functional-differential equation \[ \dot{x}(t)=f(t,x_t),\quad t\neq \tau_k, \qquad \Delta x(t)=I(t,x_t-), \quad t=\tau_k,\;\lim \tau_k=\infty. \] Applications to some population growth models with delays are also given.

MSC:

34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34K45 Functional-differential equations with impulses
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34A37 Ordinary differential equations with impulses
34D40 Ultimate boundedness (MSC2000)
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References:

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