On the Functional--integral Equation of Volterra Type With Weakly Singular Kernel

The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of $L^{α}$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.

Integral equations, Volterra equations, and the remarkable resolvent: contractions.

Burton, T.A. (2006)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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A Liapunov functional for a linear integral equation.

Burton, T.A. (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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On the Volterra integral equation with weakly singular kernel

Stanisław Szufla (2006)

Mathematica Bohemica

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