On non-linear Volterra integral-functional equations in several variables
On quadratic integral equations of Urysohn type in Fréchet spaces.
On some classes of Volterra integral equations in Banach space
On stability and robust stability of positive linear Volterra equations in Banach lattices
We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
On the application of measure of noncompactness to existence theorems
On the Aronszajn property for integral equations in Banach space
For the integral equation (1) below we prove the existence on an interval of a solution with values in a Banach space , belonging to the class , . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
On the existence and uniqueness of integrable solutions of functional equations in Banach space.
On the existence of solutions for Volterra integral inclusions in Banach spaces.
On the existence of solutions of an integro-differential equation in Banach spaces
On the existence of solutions of nonlinear integral equations in Banach spaces and Henstock-Kurzweil integrals
We prove some existence theorems for nonlinear integral equations of the Urysohn type and Volterra type , , where f and φ are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
On the existence of weak solutions of integral equations in Banach spaces
In this paper we investigate weakly continuous solutions of some integral equations in Banach spaces. Moreover, we prove a fixed point theorem which is very useful in our considerations.
On the Functional--integral Equation of Volterra Type With Weakly Singular Kernel
On the Hammerstein integral equations in Banach spaces
On the oscillatory properties of the solutions of a class of integro- differential equations of neutral type.
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 structure of -solution sets of integral equations in Banach spaces
On the structure of solutions sets of differential and 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 unique constructive solvability of Hammerstein equations.