Alexander Lomtatidze, Department of Mathematical Analysis, Faculty of Sciences, Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC
Abstract. Conditions for the existence and uniqueness of a solution of the Cauchy problem $$ u'(t)=p(t)u(\tau(t))+q(t)\,,\qquad u(a)=c\,, $$ established in , are formulated more precisely and refined for the special case, where the function $\tau$ maps the interval $]a,b[$ into some subinterval $[\tau_0,\tau_1]\subseteq[a,b]$, which can be degenerated to a point.
Keywords. First order equation, differential equation with deviating arguments, initial value problems.