Journal of Inequalities and Applications 
Volume 6 (2000), Issue 3, Pages 325-338
doi:10.1155/S1025583401000194

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

Abstract

In this paper we prove the existence theorems for the integrodifferential equation y′(t)=f(t,y(t),∫0tk(t,s,y(s))ds),  t∈I=[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.