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
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.
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.