A Note on Multistep Methods and Attracting Sets of Dynamical Systems.
A note on stability properties of integrated semigroups
A note on the asymptotic stability in the whole of non-autonomous systems.
A Note on the Covergence of Solutions of a System of Differential Equations. (Short Communication).
A Note on the Covergence of Solutions of a System of Differential Equations.
A note on the exponential stability of a matrix Riccati equation of stochastic control
A note on the fundamental matrix of variational equations in
The paper is devoted to the question whether some kind of additional information makes it possible to determine the fundamental matrix of variational equations in . An application concerning computation of a derivative of a scalar Poincaré mapping is given.
A note on the Perron instability theorem.
A note on tolerance stable dynamical systems
A partial generalization of Diliberto’s theorem for certain DEs of higher dimension
A polynomial class of Markus-Yamabe counterexamples.
In the paper [CEGHM] a polynomial counterexample to the Markus-Yamabe Conjecture and to the discrete Markus-Yamabe Question in dimension n ≥ 3 are given. In the present paper we explain a way for obtaining a family of polynomial counterexamples containing the above ones. Finally we study the global dynamics of the examples given in [CEGHM].
A predator-prey model with state dependent impulsive effects
We investigate a Lotka-Volterra predator-prey model with state dependent impulsive effects, in which the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. We present some sufficient conditions to guarantee the existence and asymptotical stability of semi-trivial periodic solutions and positive periodic solutions.
A prey-predator model with a cover linearly varying with the prey population and an alternative food for the predator.
A principle of linearization in theory of stability of solutions of variational inequalities
It is shown that the uniform exponential stability and the uniform stability at permanently acting disturbances of a sufficiently smooth but not necessarily steady-state solution of a general variational inequality is a consequence of the uniform exponential stability of a zero solution of another (so called linearized) variational inequality.
A proof existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems.
A proof of the two-dimensional Markus-Yamabe Stability Conjecture and a generalization
The following problem of Markus and Yamabe is answered affirmatively: Let f be a local diffeomorphism of the euclidean plane whose jacobian matrix has negative trace everywhere. If f(0) = 0, is it true that 0 is a global attractor of the ODE dx/dt = f(x)? An old result of Olech states that this is equivalent to the question if such an f is injective. Here the problem is treated in the latter form by means of an investigation of the behaviour of f near infinity.
A remark on exponential dichotomies.
A remark on the half-linear extension of the Hartman-Wintner theorem.
A Remark on the Oscillatoriness of Solutions of a Non-Linear Third-Order Equation
A Role of Abel's Equation in the Stabitity Theory of Differential Equations