Abstract
In the context of the nonlinear Volterra equation \( u(t) + \int _0^t b(t-s)Au(s)\mathrm{d}s \ni u_0,\) \(t\ge 0,\) with \(A\subset X \times X\) an m\(-\alpha \)-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution \(u_e\) under the assumption of the existence of a resolvent-differential \( \tilde{A} \subset X\times X\) of A at \(u_e\) with the property that \((\tilde{A}-\omega I)\) is accretive for some \(\omega >0\).
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Dedicated to Jan Prüss on the occasion of his 65th birthday
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Londen, SO., Ruess, W.M. Linearized stability for nonlinear Volterra equations. J. Evol. Equ. 17, 473–483 (2017). https://doi.org/10.1007/s00028-016-0381-z
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DOI: https://doi.org/10.1007/s00028-016-0381-z