Perturbation of linear abstract Volterra equations
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.
qualitative theory of Volterra equations
perturbation theory of integral/integro-differential equations
scientific article; zbMATH DE number 784746