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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006, Article ID 16308, 10 pages
http://dx.doi.org/10.1155/JAMSA/2006/16308

Existence of solutions to Sobolev-type partial neutral differential equations

Department of Mathematics, Indian Institute of Technology, Kanpur 208 016, India

Received 3 January 2005; Revised 30 March 2005; Accepted 31 March 2005

Copyright © 2006 Shruti Agarwal and Dhirendra Bahuguna. 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

This work is concerned with a nonlocal partial neutral differential equation of Sobolev type. Specifically, existence of the solutions to the abstract formulations of such type of problems in a Banach space is established. The results are obtained by using Schauder's fixed point theorem. Finally, an example is provided to illustrate the applications of the abstract results.