Local and global existence of solutions for a class of integro-differential equations with delay (Q635204)

The authors consider the Cauchy problem \[ y'(t)+\int_{0}^{t}K(y(t-z))y'(z)\,dz=f(t,y,y'),\quad t\geq0,\qquad y(0)=y_{0}, \] where \(K\) and \(f\) are continuous functions on \(\mathbb R\) and \({\mathbb R}^{3}\), respectively, satisfying some additional conditions. They investigate the problems of local and global existence of solutions.