## Abstract and Applied Analysis

### Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type

#### Abstract

This paper is concerned with the existence of mild and strong solutions on the interval $[0,T]$ 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 $[\delta ,T]$ for $\delta >0$ that is small enough, and, then, by letting $\delta \to 0$ and using a diagonal argument, we have the existence results on the interval $[0,T]$. 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 503656, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449678

Digital Object Identifier
doi:10.1155/2013/503656

Mathematical Reviews number (MathSciNet)
MR3134151

Zentralblatt MATH identifier
1298.34148

#### Citation

Liu, Hsiang; Liao, Cheng-Wen; Pang, Chin-Tzong. Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 503656, 12 pages. doi:10.1155/2013/503656. https://projecteuclid.org/euclid.aaa/1393449678

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