J. Nonl. Evol. Equ. Appl. 2015 (4), pp. 47-65, published on August 30, 2015:

Approximations of Solutions to Neutral Retarded Integrodifferential Equations

S. Das, D. N. Pandey, N. Sukavanam

Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand, India

Received on December 25, 2014, revised version on March 11, 2015
Accepted on March 12, 2015

Communicated by Claudio Rodrigo Cuevas Henríquez

Abstract.  This paper deals with a Sobolev type retarded integrodifferential equation. We prove existence, uniqueness and convergence of each integralapproximate solution using analytic semigroup theory and fixed point method. Then we consider Faedo-Galerkin approximation of solution and prove some convergence results. We also give some examples to illustrate the applications of the abstract results.
Keywords:Analytic semigroup; Integro-differential equation; Delay; Neutral differential equation.
2010 Mathematics Subject Classification:   34G10; 34G20; 34K30.

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