J. Nonl. Evol. Equ. Appl. 2011 (5), pp. 75-90, published on September 30, 2011:

Existence of solutions to a non-autonomous abstract neutral differential equation with deviated argument

Rajib Haloi(1), Dwijendra N. Pandey(2) and D. Bahuguna(1)

(1) Department of Mathematics and Statistics, Indian Institute of Technology Kanpur
Kanpur, Uttar Pradesh, INDIA, Pin-208016

(2) Department of Mathematics, Indian Institute of Technology Roorkee
Uttarakhand, INDIA, Pin-247667

Received June 15, 2011
Accepted September 15, 2011

Communicated by Joël Blot

Abstract.  We study the existence, uniqueness and asymptotic stability of solutions to a neutral differential equation with a deviated argument in an arbitrary Banach space. The results are obtained by applying the Sobolevskiĭ-Tanabe theory of parabolic equations, fractional powers of operators and the Banach fixed point theorem. As an application, we include an example to illustrate the theory.
Keywords: Partial functional differential equation, pseudo almost periodic solution.
2010 Mathematics Subject Classification:   34G20, 34K30, 34K40, 47N20.

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