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arXiv · 1803.10094

Existence, uniqueness, and approximation for solutions of a functional-integral equation in $L^p$ spaces

Suzete M. Afonso·Juarez S. Azevedo·Mariana P. G. da Silva·Adson M. Rocha
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Abstract

In this work we consider the general functional-integral equation: \begin{equation*} y(t) = f\left(t, \int_{a}^{b} k(t,s)g(s,y(s))ds\right), \qquad t\in [a,b], \end{equation*} and give conditions that guarantee existence and uniqueness of solution in $L^p([a,b])$, with $1<p<\infty$. We use Banach Fixed Point Theorem} and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.

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Suzete M. Afonso, Juarez S. Azevedo, Mariana P. G. da Silva, Adson M. Rocha. 2018-03-27. Existence, uniqueness, and approximation for solutions of a functional-integral equation in $L^p$ spaces. https://arxiv.org/abs/1803.10094

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