Geodesic
Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces
Electronic journal of differential equations, Tome 2003 (2003)
In this article, we prove the existence of mild and classical solutions of Sobolev type semilinear integrodifferential equations of the form

$ \frac{d}{dt}[Ex(t)] = A[x(t)+\int_0^tF(t-s)x(s)ds]+f(t,x(t)) $

in Banach spaces. The results are obtained by using the Banach contraction mapping principle and resolvent operator. An application is provided to illustrate the theory.
Classification : 34G20
Keywords: classical solution, semilinear integrodifferential equation, resolvent operator, fixed point theorem 
@article{EJDE_2003__2003__a8,
     author = {Balachandran,  Krishnan and Karunanithi,  Subbarayan},
     title = {Regularity of solutions of {Sobolev} type semilinear integrodifferential equations in {Banach} spaces},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1045.34035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a8/}
}
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Balachandran,  Krishnan; Karunanithi,  Subbarayan. Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a8/