Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 4, Pages 537-544
doi:10.1155/S1048953394000419

Well posedness for evolution inclusions

K. Balachandran1 and A. Anguraj2

1Bharathiar University, Department of Mathematics, Coimbatore 641 046, Tamil Nadu, India
2Gobi Arts College, Department of Mathematics, Gobichettipalayam 638 453, Tamil Nadu, India

Received 1 March 1993; Revised 1 May 1994

Copyright © 1994 K. Balachandran and A. Anguraj. 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

We prove the existence of a continuous selection of the multivalued map φ→Φ(φ) which is the set of all mild solutions of the evolution inclusion x(t)∈Ax(t)+F(t,x(t))+∫0th(t−s)g(x(s))dsx(0)=φ. Here F is a multivalued map, Lipschitzian with respect to x, and A is the infinitesimal generator of a C0-semigroup.