On eventual stability of impulsive systems of differential equations.
On evolution of small spheres in the phase space of a dynamical system*
We study the connection between the entropy of a dynamical system and the boundary distortion rate of regions in the phase space of the system.
On exactness of upper estimates of the characteristic exponent of a linear system with exponentially decreasing perturbations.
On Existence and Asymptotic Properties of Kneser Solutions to Singular Second Order ODE.
We investigate an asymptotic behaviour of damped non-oscillatory solutions of the initial value problem with a time singularity , , on the unbounded domain . Function is locally Lipschitz continuous on and has at least three zeros , and . The initial value . Function is continuous on has a positive continuous derivative on and . Asymptotic formulas for damped non-oscillatory solutions and their first derivatives are derived under some additional assumptions. Further, we provide...
On existence of Kneser solutions of a certain class of -th order nonlinear differential equations
The paper deals with existence of Kneser solutions of -th order nonlinear differential equations with quasi-derivatives.
On exponential dichotomy of semigroups.
On food chain in a chemostat with distinct removal rates.
On -stability of autonomous systems.
On lopsided systems.
On Lyapunov stability in hypoplasticity
We investigate the Lyapunov stability implying asymptotic behavior of a nonlinear ODE system describing stress paths for a particular hypoplastic constitutive model of the Kolymbas type under proportional, arbitrarily large monotonic coaxial deformations. The attractive stress path is found analytically, and the asymptotic convergence to the attractor depending on the direction of proportional strain paths and material parameters of the model is proved rigorously with the help of a Lyapunov function....
On Lyapunov stability of linear systems of generalized ordinary differential equations.
On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs
In this note we consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter ε. Recently, the theory of Gröbner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in ε in a neighbourhood of ε = 0. In this paper we show that the determination of the branching order and the order of the pole (if...
On oscillation criteria of fourth order linear differential equations
The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.
On oscillatory pattern of malaria dynamics in a population with temporary immunity.
On oscillatory solutions of fourth order ordinary differential equations
The paper deals with the oscillation of a differential equation as well as with the structure of its fundamental system of solutions.
On partial stability for delay systems
On peaks in carrying simplices
A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka-Volterra type that result translates into a simple condition on the coefficients.
On perturbation of continuous maps
In [1], the concept of singular isolating neighborhoods for a continuous family of continuous maps was presented. The work was based on Conley's result for a continuous family of continuous flows (cf. [2]). In this note, we study a particular family of continuous maps to illustrate the results in [1].
On perturbed iterative linear differential equations of order .
On point-dissipative systems of differential equations with quadratic nonlinearity.