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Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations. (English) Zbl 1252.34076
This paper deals with the following impulsive retarded functional differential equation (RFDE) \[ y^{\prime }(t)=f(y_{t},t),~t\neq \tau _{k}(y(t)),~t\geq t_{0}, \] \[ \Delta y(t)=I_{k}(y(t)),~t=\tau _{k}(y(t)),~k=1,2,\dots, \] with the initial condition \[ y_{t_{0}}=\phi . \] First, the concept of Lyapunov functionals for generalized ordinary differential equations is presented to obtain boundedness results. Later, some results on the boundedness of solutions of RFDE’s are obtained. Moreover, an example in the theory of a circulating fuel nuclear reactor is given.

MSC:
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34K45 Functional-differential equations with impulses
26A39 Denjoy and Perron integrals, other special integrals
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