The influence of argument delay on oscillatory properties of a second-order differential equation
The inverse carrier problem
The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.
The method of solution of the boundary value problem applied to a certain fourth order differential equation
The monotonicity of extremants of integrals of the differential equation
The multiplicity criteria for zero points of second order differential equations
The nonlinear limit-point/limit-circle problem for higher order equations
We describe the nonlinear limit-point/limit-circle problem for the -th order differential equation The results are then applied to higher order linear and nonlinear equations. A discussion of fourth order equations is included, and some directions for further research are indicated.
The oscillation of a differential equation of second order with deviating argument
The oscillation of linear first order differential systems.
The oscillatory behavior of second order nonlinear elliptic equations.
The property (A) for a certain class of the third order ODE
The Schauder-Tychonoff Fixed Point Theorem and Applications
The Sturm comparison theorem for -conjugate numbers
Theory of rapid variation on time scales with applications to dynamic equations
In the first part of this paper we establish the theory of rapid variation on time scales, which corresponds to existing theory from continuous and discrete cases. We introduce two definitions of rapid variation on time scales. We will study their properties and then show the relation between them. In the second part of this paper, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. Note...
Three point value problem for third-order linear differential equation
To conjugacy functions of second order linear differential equations
To the question of oscillation of solutions of two-dimensional differential systems with deviated arguments.
To the theory of central dispersions for the linear differential equations of a finite type-special
Total oscillatory behaviour globally in the delays
Transformation theory of linear ordinary differential equations -- from local to global investigations
A survey of investigations of linear differential equations from the point of view of transformations is described. These investigations started in the middle of the last century and continued till the present time. Essential step was done in the fifties by O. Borvka, who started global investigations of the second order equations.
Transformations and oscillatory properties of linear Hamiltonian systems -- continuous versus discret