On local attractivity and asymptotic stability of solutions of a quadratic Volterra integral equation

The existence of solutions of a nonlinear quadratic Volterra integral equation is studied. In our considerations we apply the technique of measures of noncompactness in conjunction with the classical Schauder fixed point principle. Such an approach allows us to obtain a result on the existence of solutions of an equation in question which are uniformly locally attractive or asymptotically stable.