On the oscillation of a Volterra integral equation
On the oscillatory properties of the solutions of a class of integro- differential equations of neutral type.
On the percolation of water from a cylindrical reservoir into the surrounding soil
On the positivity and zero crossings of solutions of stochastic Volterra integrodifferential equations.
On the semilinear integro-differential nonlocal Cauchy problem
In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem , x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.
On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.
On the stability of numerical methods for nonlinear Volterra integral equations.
On the strong stability of a nonlinear Volterra integro-differential system.
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.
On the Volterra integral equation with weakly singular kernel
We give sufficient conditions for the existence of at least one integrable solution of equation . Our assumptions and proofs are expressed in terms of measures of noncompactness.
On the -conditional asymptotic stability of the solutions of a nonlinear Volterra integro-differential system.
On the -stability of a nonlinear Volterra integro-differential system.
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.
Optical vortices in dispersive nonlinear Kerr-type media.
Original title unknown
Oscillatory solutions of the classical generator equation.