The authors consider initial value problems to the impulsive differential equation of the form \[ u''- f(x, u,u')=\theta,\quad x\in J,\quad x\neq x_i,\quad \Delta u|_{x=x_i}= I(u(x_i)),\quad \Delta u'|_{x= x_i}=\widetilde I(u(x_i)), \]
\[ i= 1,2,\dots, m\quad u(0)= w_0,\quad u'(0)= w_1, \] where \(f\) is a continuous function of its arguments, \(J= [0,1]\), \(I_i\) and \(\widetilde I_i\) are impulsive sources (continuous functions) propagating the impulsive effect, \(0< x_1< x_2<\cdots< x_m< 1\), are given fixed points. The authors use the coupled fixed-point theorem for mixed monotone condensing operators to obtain an interesting existence and uniqueness theorem.