On the structure of -solution sets of integral equations in Banach spaces
On the structure of the set of solutions of a Volterra integral equation in a Banach space
The set of solutions of a Volterra equation in a Banach space with a Carathéodory kernel is proved to be an , in particular compact and connected. The kernel is not assumed to be uniformly continuous with respect to the unknown function and the characterization is given in terms of a B₀-space of continuous functions on a noncompact domain.
On the Urysohn Integral Equation in Locally Convex Spaces
On the Volterra integral equation and axiomatic measures of weak noncompactness
We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness.
On the Volterra integral equation and the Henstock-Kurzweil integral.
One-dimensional model describing the non-linear viscoelastic response of materials
In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Oscillatory solutions of the classical generator equation.