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This paper is devoted to the investigation of the existence and uniqueness of a suitably defined weak solution of the abstract semilinear value problem u'(t) = Au(t) + f(t, u(t)), u(0) = x with x ϵ X, where X is a Banach space. We are concerned with two types of solutions: weak and mild. Under the assumption that A is the generator of a strongly continuous semigroup of linear, bounded operators, we...
The purpose of this paper is to present some theorems on continuity and differentiability with respect to a parameter h of a weak solution of the evolution equation u(t) = A[h]u(t) + f[h](t).
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