MATHEMATICA BOHEMICA, Vol. 131, No. 3, pp. 225-231 (2006)

On the Volterra integral equation with
weakly singular kernel

Stanislaw Szufla

Stanislaw Szufla, Faculty of Mathematics and Computer Sciences, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland

Abstract: We give sufficient conditions for the existence of at least one integrable solution of equation $x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\dd s$. Our assumptions and proofs are expressed in terms of measures of noncompactness.

Keywords: integral equation, integrable solution, measure of noncompactness

Classification (MSC2000): 45N05

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