On the solution of the Liouville equation over a rectangle.
On the Spectra of Finite-Dimensional Pertobations of Matrix Multiplication Operators.
On the spectrum of orthomorphisms and Barbashin operators.
On the spectrum of the operator which is a composition of integration and substitution
Let ϕ: [0,1] → [0,1] be a nondecreasing continuous function such that ϕ(x) > x for all x ∈ (0,1). Let the operator be defined on L₂[0,1]. We prove that has a finite number of nonzero eigenvalues if and only if ϕ(0) > 0 and ϕ(1-ε) = 1 for some 0 < ε < 1. Also, we show that the spectral trace of the operator always equals 1.
On the stability of numerical methods for nonlinear Volterra integral equations.
On the stability of Runge-Kutta methods for delay integral equations.
On the stationary solutions of Burgers' equation
On the stationary vibrations of a rectangular plate subjected to stress prescribed partially at the circumference.
On the strong convergence to equilibrium of the Foiaş solutions of the transport equation
We define the Foiaş solutions of the transport equation and we prove that the strong asymptotic stability of the Foiaş solutions is equivalent to the asymptotic stability of the solutions of the transport equation in L¹.
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 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 Tjon-Wu representation of the Boltzmann equation
On the two-fold symbol chain of a C*-algebra of singular integral operators on a polycylinder.
On the unique constructive solvability of Hammerstein equations.
On the unique solvability of a nonlocal phase separation problem for multicomponent systems
A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential...
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.