In this paper, we study a class of neutral functional integrodifferential equations with finite delay in Banach spaces. We are interested in the global existence, uniqueness of mild solutions with values in the Banach space and in its subspace $D(A).$ The results are based on Banach's and Schauder's fixed point theorems and on the technique of equivalent norms. As an application, we consider a diffusion neutral functional integrodifferential equation.
Mild solution, functional integrodifferential equation, neutral equation, semigroup of bounded linear operators, infinitesimal generator, finite delay
KOUMLA, SYLVAIN; PRECUP, RADU; and SENE, ABDOU
"Existence resultsfor some neutral functional integrodifferential equations with bounded delay,"
Turkish Journal of Mathematics: Vol. 43:
4, Article 1.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss4/1