[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2014.27.1.89

EXISTENCE OF SOLUTIONS IN THE α-NORM FOR NEUTRAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

Choi, Sung Kyu (Department of Mathematics Chungnam National University)
Jang, Hyun Ho (Department of Mathematics Chungnam National University)
Koo, Namjip (Department of Mathematics Chungnam National University)
Yun, Chanmi (Department of Mathematics Chungnam National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.27, no.1, 2014 , pp. 89-97 More about this Journal

Abstract

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$ -norm.

Keywords

mild solution; neutral integrodifferential equation; non-local condition; ${\alpha}$ -norm; fractional power of operator; resolvent operator;

Citations & Related Records

Reference

1	R. Benkhalti and K. Ezzinbi, Existence and stability in the ${\alpha}$ -norm for some partial functional differential equations with infinite delay, Differential and Integral Equ. 19 (2006), 545-572.
2	H. Bouzahir, Partial Neutral Functional Differential Equations with Infinite Delay, VDM Verlag Dr. Muller, Saarbrucken, 2010.
3	L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505. DOI
4	K. Ezzinbi, X. Fu, and K. Hilal, Existence and regularity in the ${\alpha}$ -norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Anal. 67 (2007), 1613-1622. DOI ScienceOn
5	X. Fu, On solutions of neutral nonlocal evolution equations with nondense domain, J. Math. Anal. Appl. 299 (2004), 392-410. DOI ScienceOn
6	X. Fu, Y. Gao, and Y. Zhang, Existence of solutions for neutral integrodifferential equations with nonlocal conditions, Taiwanese J. Math. 16 (2012), 1879-1909. DOI
7	K. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000.
8	A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.