On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals

Aneta Sikorska-Nowak. "On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals." Annales Polonici Mathematici 83.3 (2004): 257-267. <http://eudml.org/doc/280326>.

@article{AnetaSikorska2004,
abstract = {We prove some existence theorems for nonlinear integral equations of the Urysohn type $x(t) = φ(t) + λ∫_0^a f(t,s,x(s))ds$ and Volterra type $x(t) = φ(t) + ∫_0^tf(t,s,x(s))ds$, $t ∈ I_a = [0,a]$, where f and φ 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 = {Annales Polonici Mathematici},
keywords = {existence; measure of noncompactness; nonlinear Volterra integral equation; nonlinear Urysohn integral equation; Henstock-Kurzweil integral; Banach spaces},
language = {eng},
number = {3},
pages = {257-267},
title = {On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals},
url = {http://eudml.org/doc/280326},
volume = {83},
year = {2004},
}

TY - JOUR
AU - Aneta Sikorska-Nowak
TI - On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals
JO - Annales Polonici Mathematici
PY - 2004
VL - 83
IS - 3
SP - 257
EP - 267
AB - We prove some existence theorems for nonlinear integral equations of the Urysohn type $x(t) = φ(t) + λ∫_0^a f(t,s,x(s))ds$ and Volterra type $x(t) = φ(t) + ∫_0^tf(t,s,x(s))ds$, $t ∈ I_a = [0,a]$, where f and φ 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; measure of noncompactness; nonlinear Volterra integral equation; nonlinear Urysohn integral equation; Henstock-Kurzweil integral; Banach spaces
UR - http://eudml.org/doc/280326
ER -