Existence theory for nonlinear Volterra integral and differential equations (Q5952859)

The technique of measures of noncompactness and measures of weak noncompactness is used in order to derive existence results for integrodifferential equation of the form \[ y'(t)= f\left(t,y(t), \int^t_0 k\bigl(t,s,y(s)\bigr)ds \right),\;t\in[0,T],\;y(0)=0. \tag{1} \] Here it is assumed that the functions \(k\), \(f\) take values in a Banach space and are Carathéodory functions (in terms of continuity or weak sequential continuity). Moreover, some requirements expressed in terms of measures of noncompactness or measures of weak noncompactness are also imposed.