Perturbations of Systems Describing the Motion of a Particle in Central Fields
The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.
Phasenraum-Methoden zum Studium nichtlinearer Differentialgleichungen.
Pinning lag synchronization between two dynamical networks with non-derivative and derivative couplings
In this paper, we study lag synchronization between two dynamical networks with non-derivative and derivative couplings via pinning control. We design two types of pinning control schemes, including linear and adaptive feedback controllers. With the corresponding control algorithms, we obtain two theorems on the lag synchronization based on Schur complement and Barbalat's lemma. In addition, we obtain the domain for the linear feedback gains. Finally, we provide two numerical examples to show the...
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
Polynomial asymptotic stability of damped stochastic differential equations.
Polynomial expansiveness and admissibility of weighted Lebesgue spaces
The paper investigates the interaction between the notions of expansiveness and admissibility. We consider a polynomially bounded discrete evolution family and define an admissibility notion via the solvability of an associated difference equation. Using the admissibility of weighted Lebesgue spaces of sequences, we give a characterization of discrete evolution families which are polynomially expansive and also those which are expansive in the ordinary sense. Thereafter, we apply the main results...
Population dynamics of Bithynia tentaculata
Positive decreasing solutions of systems of second order singular differential equations.
Positive solutions of third order damped nonlinear differential equations
We study solutions tending to nonzero constants for the third order differential equation with the damping term in the case when the corresponding second order differential equation is oscillatory.
Positive solutions to second-order singular differential equations involving the one-dimensional -Laplace operator.
Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems
In this paper we consider positive unbounded solutions of second order quasilinear ordinary differential equations. Our objective is to determine the asymptotic forms of unbounded solutions. An application to exterior Dirichlet problems is also given.
Positively homogeneous functions and the Łojasiewicz gradient inequality
It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.
Positivity and stability for a system of transport equations with unbounded boundary perturbations.
Power bounded and exponentially bounded matrices
The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.
Poznámka o jistých nelineárních diferenciálních rovnicích 3. a 4. řádu
Practical -stability behavior of time-varying nonlinear systems
We deal with the problem of practical uniform -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results.
Practical Lyapunov stability criteria for differential algebraic equations
Practical Stability in Terms of Two Measures for Hybrid Dynamic Systems
We study hybrid dynamic systems on time scales. Using Lyapunov-like functions, we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales.
Problème général de la stabilité du mouvement
Propriétés asymptotiques d'un système d'équations différentielles