On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock–Kurzweil integrals
Volume 83 / 2004
Annales Polonici Mathematici 83 (2004), 257-267
MSC: Primary 34G20, 28B05, 45D05.
DOI: 10.4064/ap83-3-7
Abstract
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.
