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On a nonlinear abstract Volterra equation. (English) Zbl 1334.45004

Summary: Existence of solutions is shown for equations of the type \(Av+B(KGv,v)=f\), where \(A\), \(B\) and \(G\) are possibly nonlinear operators acting on a Banach space \(V\), and \(K\) is a Volterra operator of convolution type. The proof relies on the convergence of a suitable time discretization scheme.

MSC:

45D05 Volterra integral equations
47J35 Nonlinear evolution equations
65J08 Numerical solutions to abstract evolution equations
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References:

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