Taiwanese Journal of Mathematics

EXISTENCE OF SOLUTIONS FOR NEUTRAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

Xianlong Fu, Yan Gao, and Yu Zhang

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Abstract

This paper is concerned with the existence of mild solutions, strong solutions and strict solutions for a class of neutral integrodifferential equations with nonlocal conditions in Banach space. Since the nonlinear terms of the systems involve spacial derivatives, the theory of fractional power and $\alpha$-norm is used to discuss the problem. In the end an example is provided to illustrate the applications of the obtained results.

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1879-1909.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406803

Digital Object Identifier
doi:10.11650/twjm/1500406803

Mathematical Reviews number (MathSciNet)
MR2970691

Zentralblatt MATH identifier
1259.34076

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 34K40: Neutral equations 35R09: Integro-partial differential equations [See also 45Kxx] 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 47N20: Applications to differential and integral equations

Keywords
neutral integrodifferential equation analytic semigroup resolvent operator fractional power operator nonlocal condition

Citation

Fu, Xianlong; Gao, Yan; Zhang, Yu. EXISTENCE OF SOLUTIONS FOR NEUTRAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS. Taiwanese J. Math. 16 (2012), no. 5, 1879--1909. doi:10.11650/twjm/1500406803. https://projecteuclid.org/euclid.twjm/1500406803


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