An Lp-Analogue of the Weyl Alternative.
An ordinary differential equation homeomorphic with an essential control system
An oscillation criterion for a canonical form of third order linear differential equations
An oscillation criterion for -th order nonlinear differential equations with retarded arguments
An oscillation criterion for nonlinear third-order differential equations.
An oscillation criterion for third order linear differential equations
An oscillation theorem for a second order nonlinear differential equations with variable potential.
An oscillation theorem for higher order nonhomogeneous superlinear differential equations.
An oscillatory half-linear differential equation
A second-order half-linear ordinary differential equation of the type is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of zeros of its solutions can also be established.
Analysis of a single species with diffusion in a polluted environment.
Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry
Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local...
Analysis of Synchronization in a Neural Population by a Population Density Approach
In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate...
Analysis of the predator-prey model with climax prey population
The aim of the contribution is to study ODE predator-prey system with a prey population embodying the Allee effect. Particular stationary points are analyzed and the results are illustrated by graphs of numerical solutions for various values of model parameters.
Analytic First Integrals of Ordinary Differential Equations
Analytic results for oscillatory systems with extremal dynamic properties
Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics.
Angenäherte Schwingungsfrequenzformeln für konservative Systeme (4)
Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth
We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe the neoplastic...
Another proof of Borůvka's criterion on global equivalence of the second order ordinary linear differential equations
Another representation for the maximal Lie algebra of in terms of operators.