On transformations of differential equations and systems with deviating argument
On transformations of self-adjoint linear differential systems and their reciprocals
On transformations of self-adjoint linear differential systems
On transformations of singular quadratic functionals corresponding to equation
On transformations of two homogeneous linear second order differential equations of a general and of Sturm forms
On two-dimensional linear spaces of continuous functions of the same character
On unbounded nonoscillatory solutions of systems of neutral differential equations
On unbounded positive solutions of nonlinear differential equations with oscillating coefficients
On unbounded solutions for differential equations with mean curvature operator
We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived.
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.