Volterra and Urysohn integral equations in Banach spaces.

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.

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

Aldona Dutkiewicz (2008)

Publications de l'Institut Mathématique

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Existence theory for nonlinear Volterra integral and differential equations.

Sikorska, Aneta (2001)

Journal of Inequalities and Applications [electronic only]

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Integral equivalence between a nonlinear system and its nonlinear perturbation

Alexander Haščák (1984)

Mathematica Slovaca

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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.