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2013 Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type
Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang
Abstr. Appl. Anal. 2013(SI45): 1-12 (2013). DOI: 10.1155/2013/503656

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 [ δ , T ] for δ > 0 that is small enough, and, then, by letting δ 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.

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Hsiang Liu. Cheng-Wen Liao. Chin-Tzong Pang. "Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type." Abstr. Appl. Anal. 2013 (SI45) 1 - 12, 2013. https://doi.org/10.1155/2013/503656

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1298.34148
MathSciNet: MR3134151
Digital Object Identifier: 10.1155/2013/503656

Rights: Copyright © 2013 Hindawi

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