Journal of Applied Analysis 08 (2002), No. 1, 083--110
Copyright Heldermann Verlag 2002
Linear Fredholm Integral Equations and the Integral of Kurzweil
Marcia Cristina Federson
Inst. Ciencias Matemáticas Computacao, Universidade de Sao Paulo, Sao Carlos SP 13560-970, Brazil
Ricardo Bianconi
Inst. Matemática Estatistica, Universidade de Sao Paulo, Sao Carlos SP 13560-970, Brazil
[Abstract-pdf]
We apply the Kurzweil-Henstock integral setting to prove a Fredholm Alternative-type result for the integral equation \[ x\left( t\right) -\,^{K}\int_{\left[ a,b\right] }\alpha \left( t,s\right) x\left( s\right) ds=f\left( t\right) ,\quad t\in \left[ a,b\right] , \] where $x$ and $f$ are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval $\left[ a,b\right] $ of the real line with values on Banach spaces. An application is given.
Keywords: Linear integral equations, Fredholm Alternative, Kurzweil-Henstock integrals.
MSC: 45A05; 45B05, 26A39
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