On the exactness of the Kiguradze-Kvinikadze blow-up condition for nonlinear ordinary differential equations

We show the exactness of the Kiguradze–Kvinikadze blow-up condition for solutions of the Cauchy problem $$w^{(m)}=f(t,w,\dots ,w^{(m-1)}),w^{(i)}(0)=a_i\ge 0,i=0,\dots ,m-1.$$