Geodesic
On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals
Aneta Sikorska-Nowak1
1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland
Annales Polonici Mathematici, Tome 83 (2004) no. 3, pp. 257-267

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove some existence theorems for nonlinear integral equations of the Urysohn type $x(t)=\varphi (t)+\lambda \int _0^a f(t,s,x(s))\, ds$ and Volterra type $x(t)=\varphi (t)+\int _0^tf(t,s,x(s))\, ds$, $t\in I_a=[0,a]$, where $f$ and $\varphi $ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock–Kurzweil integral.
DOI : 10.4064/ap83-3-7
Keywords: prove existence theorems nonlinear integral equations urysohn type varphi lambda int s volterra type varphi int s where varphi functions values banach spaces fundamental tools measures noncompactness properties henstock kurzweil integral

Aneta Sikorska-Nowak 1

1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland 
@article{10_4064_ap83_3_7,
     author = {Aneta Sikorska-Nowak},
     title = {On the existence of solutions
 of nonlinear integral equations in {Banach} spaces
 and {Henstock{\textendash}Kurzweil} integrals},
     journal = {Annales Polonici Mathematici},
     pages = {257--267},
     publisher = {mathdoc},
     volume = {83},
     number = {3},
     year = {2004},
     doi = {10.4064/ap83-3-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap83-3-7/}
}
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
SP  - 257
EP  - 267
VL  - 83
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap83-3-7/
DO  - 10.4064/ap83-3-7
LA  - en
ID  - 10_4064_ap83_3_7
ER  - 
%0 Journal Article
%A Aneta Sikorska-Nowak
%T On the existence of solutions
 of nonlinear integral equations in Banach spaces
 and Henstock–Kurzweil integrals
%J Annales Polonici Mathematici
%D 2004
%P 257-267
%V 83
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap83-3-7/
%R 10.4064/ap83-3-7
%G en
%F 10_4064_ap83_3_7
Aneta Sikorska-Nowak. On the existence of solutions
 of nonlinear integral equations in Banach spaces
 and Henstock–Kurzweil integrals. Annales Polonici Mathematici, Tome 83 (2004) no. 3, pp. 257-267. doi: 10.4064/ap83-3-7

Cité par Sources :