Solutions of Hammerstein equations in the space (Λ_1,Λ_2)BV(I^b_a)

Meimei Song, Jinpeng Liu

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.

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Published: 2020-06-18

How to Cite this Article:

Meimei Song, Jinpeng Liu, Solutions of Hammerstein equations in the space (Λ_1,Λ_2)BV(I^b_a), Adv. Fixed Point Theory, 10 (2020), Article ID 14

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.

Advances in Fixed Point Theory

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