Solutions of Hammerstein equations in the space (Λ_1,Λ_2)BV(I^b_a)
Abstract
In this paper, we study the form of Hammerstein integral equations
$u(x)=v(x)+\lambda\int_{I^{b}_{a}}k(x,y)f(y,u(y))dy,(\lambda\in\mathbb{R})$
and Volterra Hammerstein integral equations in the condition of two-variables. Show the definition of $(\Lambda_{1},\Lambda_{2})$ bounded variation, write as $(\Lambda_{1},\Lambda_{2})BV(I^{b}_{a})$. If $v$, $k$ are $(\Lambda^{(1)},\Lambda^{(2)})BV(I^{b}_{a};\mathbb{R})$ functions and $f$ is a locally Lipschitz function, there exists a number $\rho>0$ such that when $|\lambda|<\rho$, Hammerstein integral equations has a unique solution. Give the proof and extend.Copyright © 2020 Meimei Song, Jinpeng Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
M. Song, J. Liu, Solutions of Hammerstein equations in the space (Λ_1,Λ_2)BV(I^b_a), Adv. Fixed Point Theory 10 (2020), 14. https://doi.org/10.28919/afpt/4702
BibTeX
@article{Song2020,
author = {Song, Meimei and Liu, Jinpeng},
title = {Solutions of Hammerstein equations in the space (Λ_1,Λ_2)BV(I^b_a)},
journal = {Adv. Fixed Point Theory},
volume = {10},
year = {2020},
pages = {14},
doi = {10.28919/afpt/4702}
}