1/1

Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in Lp Spaces

dataset
posted on 25.12.2019 by S. M. AFONSO, J. S. AZEVEDO, M. P. G. DA SILVA, A. M. ROCHA

ABSTRACT In this work we consider the general functional-integral equation: y ( t ) = f ( t , ∫ 0 1 k ( t , s ) g ( s , y ( s ) ) d s ) , t ∈ [ 0 , 1 ] , and give conditions that guarantee existence and uniqueness of solution in L p ( [ 0 , 1 ] ), with 1 1 p ∞.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.

History

Licence

Exports