Lower bounds for solutions to a class of nonlinear integrodifferential equations in hilbert space

Abstract

Growth estimates are obtained for solutions of the abstract nonlinear initial-value problem

where H ₊ is a Hilbert subspace of some real Hilbert space H, with topologically as well as algebraically, and with H _{_} being the dual of H ₊ via the inner product of H and denoting the space of all bounded symmetric linear operators from H ₊ into H _{_}.