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Authors
Affiliations
1 Department of Mathematics with Computer Applications, Kongunadu Arts and Science College, Coimbatore, IN
Source
Fuzzy Systems, Vol 3, No 9 (2011), Pagination: 395-400
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.
Keywords
Banach Fixed Point Theorem, Integro Differential Equations, Gronwall’s Inequality, Semi Groups.
