On the Hammerstein equation in the space of functions of bounded $\varphi$-variation in the plane

@article{Azócar2013,
abstract = {In this paper we study existence and uniqueness of solutions for the Hammerstein equation \[ u(x) = v(x) + \lambda \int \_\{I\_\{a\}^\{b\}\} K(x,y) f\big (y,u(y)\big )\, dy\,, \quad x \in I\_\{a\}^\{b\} := [a\_\{1\},b\_\{1\}] \times [a\_\{2\},b\_\{2\}]\,, \] in the space $BV_\{\varphi \}^\{\mathbb \{R\}\}(I_\{a\}^\{b\})$ of function of bounded total $\varphi -$variation in the sense of Riesz, where $ \lambda \in \mathbb \{R\} $, $ K \colon I_\{a\}^\{b\} \times I_\{a\}^\{b\} \rightarrow \mathbb \{R\} $ and $ f\colon I_\{a\}^\{b\} \times \mathbb \{R\} \rightarrow \mathbb \{R\}$ are suitable functions.},
author = {Azócar, Luis, Leiva, Hugo, Matute, Jesús, Merentes, Nelson},
journal = {Archivum Mathematicum},
keywords = {existence and uniqueness of solutions of the Hammerstein integral equation in the plane; $\varphi $-bounded total variation norm on a rectangle; existence; uniqueness; Hammerstein integral equation in the plane; -bounded total variation norm on a rectangle; nonlinear Leray-Schauder type alternative},
language = {eng},
number = {1},
pages = {51-64},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the Hammerstein equation in the space of functions of bounded $\varphi $-variation in the plane},
url = {http://eudml.org/doc/252518},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Azócar, Luis
AU - Leiva, Hugo
AU - Matute, Jesús
AU - Merentes, Nelson
TI - On the Hammerstein equation in the space of functions of bounded $\varphi $-variation in the plane
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 1
SP - 51
EP - 64
AB - In this paper we study existence and uniqueness of solutions for the Hammerstein equation \[ u(x) = v(x) + \lambda \int _{I_{a}^{b}} K(x,y) f\big (y,u(y)\big )\, dy\,, \quad x \in I_{a}^{b} := [a_{1},b_{1}] \times [a_{2},b_{2}]\,, \] in the space $BV_{\varphi }^{\mathbb {R}}(I_{a}^{b})$ of function of bounded total $\varphi -$variation in the sense of Riesz, where $ \lambda \in \mathbb {R} $, $ K \colon I_{a}^{b} \times I_{a}^{b} \rightarrow \mathbb {R} $ and $ f\colon I_{a}^{b} \times \mathbb {R} \rightarrow \mathbb {R}$ are suitable functions.
LA - eng
KW - existence and uniqueness of solutions of the Hammerstein integral equation in the plane; $\varphi $-bounded total variation norm on a rectangle; existence; uniqueness; Hammerstein integral equation in the plane; -bounded total variation norm on a rectangle; nonlinear Leray-Schauder type alternative
UR - http://eudml.org/doc/252518
ER -