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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