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Existence and Uniqueness of Solutions of a Semi Linear Evolution Integro-Differential Equations
Abstract
In this paper we consider the boundary value problem for the first order nonlinear integro differential equation of the form,
Where –A is the infinitesimal generator of a C0 semigroup T(t), t≥0 on a Banach space X, and f : [t0,t0+a] x X x X x X→X , g(t1,…tp,u(.)) : X→X are the given functions.
We prove the existence and uniqueness of mild, strong and classical solutions of the above integro-differential equation by using the method of semigroups and the Banach fixed point theorem.
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References
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