Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals

Aneta Sikorska-Nowak. "Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals." Commentationes Mathematicae 47.2 (2007): null. <http://eudml.org/doc/291471>.

@article{AnetaSikorska2007,
abstract = {We prove an existence theorems for the nonlinear integral equation \[ x(t) = f (t) + \int \_\{0\}^a k\_1 (t, s)x(s)ds + \int \_\{0\}^a k\_2(t, s)g(s, x(s))ds,\quad t \in I\_a = [0, a], a \in \mathbb \{R\} \_+, \] where $f, g, x$ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.},
author = {Aneta Sikorska-Nowak},
journal = {Commentationes Mathematicae},
keywords = {existence of solution; measure of noncompactness; nonlinear Fredholm integral equation; Henstock-Kurzweil integral; HL integral},
language = {eng},
number = {2},
pages = {null},
title = {Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals},
url = {http://eudml.org/doc/291471},
volume = {47},
year = {2007},
}

TY - JOUR
AU - Aneta Sikorska-Nowak
TI - Existance of solutions of nonlinear integral equations and Henstock–Kurzweil integrals
JO - Commentationes Mathematicae
PY - 2007
VL - 47
IS - 2
SP - null
AB - We prove an existence theorems for the nonlinear integral equation \[ x(t) = f (t) + \int _{0}^a k_1 (t, s)x(s)ds + \int _{0}^a k_2(t, s)g(s, x(s))ds,\quad t \in I_a = [0, a], a \in \mathbb {R} _+, \] where $f, g, x$ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
LA - eng
KW - existence of solution; measure of noncompactness; nonlinear Fredholm integral equation; Henstock-Kurzweil integral; HL integral
UR - http://eudml.org/doc/291471
ER -