On unbounded positive solutions of nonlinear differential equations with oscillating coefficients
On uniform exponential stability of periodic evolution operators in Banach spaces.
On unstable neutral differential equations of the second order
The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation to be oscillatory and to improve some existing results. The main results are based on the comparison principles.
On using curvature to demonstrate stability.
On vanishing at infinity of solutions of ordinary differential equations
On zeros of solutions of the differential equation
On zeros of solutions of the differential equation
On zeros of solutions to a second-order singular half-linear equation.
On -bounded solutions for non-homogeneous matrix Lyapunov systems on .
On -limit sets of nonautonomous differential equations
In this paper the -limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of -limit sets and a Poincar’e-Bendixon type theorem.
One-parameter families of brake orbits in dynamical systems
We give a clear and systematic exposition of one-parameter families of brake orbits in dynamical systems on product vector bundles (where the fiber has the same dimension as the base manifold). A generalized definition of a brake orbit is given, and the relationship between brake orbits and periodic orbits is discussed. The brake equation, which implicitly encodes information about the brake orbits of a dynamical system, is defined. Using the brake equation, a one-parameter family of brake orbits...
One-parameter family of cubic Kolmogorov system with an isochronous center.
We show the existence of a one-parameter family of cubic Kolmogorov system with an isochronous center in the realistic quadrant.
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Optimal conditions for maximum and antimaximum principles of the periodic solution problem.
Optimal impulsive harvest policy for time-dependent logistic equation with periodic coefficients.
Optimal oscillatory time for a class of second order nonlinear dissipative ODE
Orbites Hétérocliniques au Voisinage d'une Bifurcation de Poincaré Dégénérée pour les Champs de Vecteurs de ...
Orbites périodiques des systèmes hamiltoniens du type de celui des trois corps
Orbites périodiques d'un système hamiltonien du voisinage d'un point d'équilibre
Orbits connecting singular points in the plane
This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.