Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations (Q2883878)

This paper deals with the following impulsive retarded functional differential equation (RFDE) NEWLINE\[NEWLINEy^{\prime }(t)=f(y_{t},t),~t\neq \tau _{k}(y(t)),~t\geq t_{0},NEWLINE\]NEWLINE NEWLINE\[NEWLINE\Delta y(t)=I_{k}(y(t)),~t=\tau _{k}(y(t)),~k=1,2,\dots,NEWLINE\]NEWLINE with the initial condition NEWLINE\[NEWLINEy_{t_{0}}=\phi .NEWLINE\]NEWLINE 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.