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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2013; 50(3): 627-639

Printed May 1, 2013

https://doi.org/10.4134/JKMS.2013.50.3.627

Copyright © The Korean Mathematical Society.

Semilinear nonlocal differential equations with delay terms

Jin-Mun Jeong and Su Jin Cheon

Pukyong National University, Pukyong National University

Abstract

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The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H\"older continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

Keywords: asemilinear differential equation, nonlocal condition, delay term, fundamental solution, regularity for solutions

MSC numbers: Primary 35F25, 35K55

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