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Abstract and Applied Analysis
Volume 2013, Article ID 503656, 12 pages
Research Article

Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type

Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Taoyuan 320, Taiwan

Received 13 August 2013; Accepted 22 September 2013

Academic Editor: Ngai-Ching Wong

Copyright © 2013 Hsiang Liu et al. 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.


This paper is concerned with the existence of mild and strong solutions on the interval for some neutral partial differential equations with nonlocal conditions. The linear part of the equations is assumed to generate a compact analytic semigroup of bounded linear operators, whereas the nonlinear part satisfies the Carathëodory condition and is bounded by some suitable functions. We first employ the Schauder fixed-point theorem to prove the existence of solution on the interval for that is small enough, and, then, by letting and using a diagonal argument, we have the existence results on the interval . This approach allows one to drop the compactness assumption on a nonlocal condition, which generalizes recent conclusions on this topic. The obtained results will be applied to a class of functional partial differential equations with nonlocal conditions.