Linear Fredholm integral equations and the integral of Kurzweil. (English) Zbl 1043.45010

Federson, M.; Bianconi, R.

J. Appl. Anal. 8, No. 1, 83-110 (2002).

Fredholm integral equations of the second kind of vector-valued functions (in Banach spaces) with Kurzweil or Henstock integrals are considered. A Fredholm alternative is proved and a corresponding ‘adjoint’ equation is obtained. The results are applied for boundary value problems on intervals.

Reviewer: Martin Väth (Würzburg)

MSC:

45N05	Abstract integral equations, integral equations in abstract spaces
34B05	Linear boundary value problems for ordinary differential equations
45B05	Fredholm integral equations
26A39	Denjoy and Perron integrals, other special integrals

Keywords:

Fredholm integral equation; Fredholm alternative; Kurzweil integral; Henstock integral; Banach spaces; boundary value problems

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