On the Darboux transformation. II.
Automorphisms of the family of all Sturm-Liouville equations are investigated. The classical Darboux transformation arises as a particular case of a general result.
On the decay rate of solutions of non-autonomous differential systems.
On the definition of strange nonchaotic attractor
The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove that a whole...
On the delay differential equation y'(x) = ay(τ(x)) + by(x)
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation . Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.
On the density of extremal solutions of differential inclusions
An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].
On the density of the range for some nonlinear operators
On the dependence of solutions upon the right hand side of an ordinary differential equation.
On the determination of the potential function from given orbits
The paper deals with the problem of finding the field of force that generates a given ()-parametric family of orbits for a mechanical system with degrees of freedom. This problem is usually referred to as the inverse problem of dynamics. We study this problem in relation to the problems of celestial mechanics. We state and solve a generalization of the Dainelli and Joukovski problem and propose a new approach to solve the inverse Suslov’s problem. We apply the obtained results to generalize the...
On the differential form spectrum of hyperbolic manifolds
We give a lower bound for the bottom of the differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.
On the differential operators with periodic matrix coefficients.
On the dimension of the solution set to the homogeneous linear functional differential equation of the first order
Consider the homogeneous equation where is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.
On the direction of pitchfork bifurcation.
On the discrete kinetic theory for active particles. Modelling the immune competition.
On the discreteness of the spectra of the Dirichlet and Neumann -biharmonic problems.
On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
On the discretization of degenerate sweeping processes.
On the dispersion structure of the differential equation y"=q(t)y having in the generalized Floquet theory the same characteristic multipliers
On the distribution of zeros of solutions of some types of differential equation
On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators.
On the Dynamics of a Two-Strain Influenza Model with Isolation
Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling...