A class of the first order impulsive dynamic equations on time scales (Q949705)

The authors consider the following problem on time scales: \[ \begin{aligned} &y^\Delta(t)+ p(t) y^\sigma(t)= f(t,y(t)), \quad t\in T=[a,b],\;t\neq t_k,\;k=1,2,\dots,m, \tag{1}\\ &y(t_k^+)= I_k(t_k^-)), \quad k=1,\dots,m,\tag{2}\\ &y(a)= \eta. \tag{3}\end{aligned} \] By means of fixed-point theorems, sufficient conditions for the existence of a unique solution of (1)--(3) are derived.