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Existence and Uniqueness of Solutions of a Semi Linear Evolution Integro-Differential Equations


Affiliations
1 Department of Mathematics with Computer Applications, Kongunadu Arts and Science College, Coimbatore, India
     

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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.
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  • Existence and Uniqueness of Solutions of a Semi Linear Evolution Integro-Differential Equations

Abstract Views: 246  |  PDF Views: 1

Authors

S. Dhanalakshmi
Department of Mathematics with Computer Applications, Kongunadu Arts and Science College, Coimbatore, India

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.