On abstract Volterra equations with kernels having a positive resolvent |
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Authors: | Ph. Clément |
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Affiliation: | 1. Technische Hogeschool te Delft, 2628 B2, Delft, The Netherlands
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Abstract: | We consider the nonlinear abstract Volterra equation of convolution type: V $$u(t) + b * Au(t) = u_0 + b * g(t), t geqq 0,$$ whereA ism-accretive in Banach spaceX, b is a given real kernel,u 0 andg are given. Boundedness and asymptotic properties of the solutions are established under the assumption that the kernel satisfies certain natural positivity conditions. |
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