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Perturbation of linear abstract Volterra equations. (English) Zbl 0824.45013
The aim of this paper is to discuss perturbed equations associated with abstract Volterra equations. We will consider only the case when the unperturbed equation is linear, namely, (1) \(x(t)= (Lx)(t)+ (Nx)(t)\), or (2) \(\dot x(t)= (Lx)(t)+ (Nx)(t)\).
In both equations (1) and (2), \(L\) stands for a linear abstract Volterra operator acting on some function space, while \(N\) denotes a nonlinear operator acting on the same or another function space, not necessarily of Volterra type. Of course, when \(N\) is also a Volterra (abstract) operator, the equations (1) and (2) are both of Volterra type.

MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
45J05 Integro-ordinary differential equations
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