Solutions of the Hammerstein equations in $BV_\varphi(I_{a}^{b},\, \mathbb{R})

Wadie Aziz; José Guerrero; L. Azócar; Nelson Merentes

ArticleOriginal scientific text

Title

Solutions of the Hammerstein equations in !$!BV_\varphi(I_{a}^{b},\, \mathbb{R})

Authors ¹, ², ³, ⁴

Affiliations

Universidad de Los Andes Departamento de Física y Matemática Trujillo-Venezuela
Universidad Nacional Experimental del Táchira Departamento de Matemática y Física San Cristóbal-Venezuela
Universidad Nacional Abierta Area de Matem´atica, Caracas-Venezuela ´
Universidad Central de Venezuela Escuela de Matemáticas, Caracas-Venezuela

Abstract

In this paper we study existence and uniqueness of solutions for the Hammerstein equation

u (x) = v (x) + λ \int_{I_{a}^{b}} K (x, y) f (y, u (y)) d y

\noi in the space of function of bounded total

φ

-variation in the sense of Hardy-Vitali-Tonelli, where

λ \in R

,

K : I_{a}^{b} \times I_{a}^{b} l o n g \to R

and

f : I_{a}^{b} \times R l o n g \to R

are suitable functions. The existence and uniqueness of solutions are proved by means of the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle.

Keywords

ENG

Hammerstein integral equation, Banach spaces, bounded

φ

-variation in the sense of Hardy-Vitali-Tonelli, Banach's contraction principle, Leray-Schauder nonlinear alternative principle

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Title

Solutions of the Hammerstein equations in !$!BV_\varphi(I_{a}^{b},\, \mathbb{R})

Affiliations

Abstract

Keywords

Bibliography