Journal of Inequalities and Applications
Volume 6 (2000), Issue 3, Pages 325-338

Existence theory for nonlinear volterra integral and differential equations

Aneta Sikorska

Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki48/49, Poznań 60-769, Poland

Received 28 July 1999; Revised 6 January 2000

Copyright © 2000 Aneta Sikorska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we prove the existence theorems for the integrodifferential equation y(t)=f(t,y(t),0tk(t,s,y(s))ds),tI=[0,T],y(0)=y0, where in first part f,k,y are functions with values in a Banach space E and the integral is taken in the sense of Bochner. In second part f,k are weakly–weakly sequentially continuous functions and the integral is the Pettis integral. Additionaly, the functions f and k satisfy some boundary conditions and conditions expressed in terms of measure of noncompactness or measure of weak noncompactness.