Some results of differentiability for the solution of an integral equations system


Dobrițoiu, Maria


Abstract

carpathian_2014_30_2_147_159_abstract

Using the fixed point theorem given by [Rus, I. A., A Fiber generalized contraction theorem and applications, Mathematica, 41(64) (1999), No. 1, 85–90] and an idea of [Sotomayor, J., Smooth dependence of solution of differential equation on initial data: a simple proof, Bol. Soc. Brasil., 4 (1973), No. 1, 55–59] we establish some conditions of differentiability of the solution for the following system of integral equations:
x(t)=∫abK(t,s)⋅h(s,x(s),x(a),x(b))ds+f(t),t∈[a,b],
x(t)=∫abK(t,s)⋅h(s,x(s),x(a),x(b))ds+f(t),t∈[a,b],
and such we obtain two theorems of differentiability. Finally, two examples are given.

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Author(s)

Dobrițoiu, Maria