Phase and dispersion theory of the differential equation in connection with the generalized Floquet theory
Phase matrix of linear differential systems
Pointwise transformations of linear differential equations
Polynomial operator matrices as semigroup generators: the 2 x 2 case.
Positivity of the Green functions for higher order ordinary differential equations.
Power bounded prolongations and Picard-Lindelöf iteration.
Poznámka k integrování některých differenciálních rovnic lineárních
Poznámky o charakteristické rovnici jisté transformace
Practical -stability behavior of time-varying nonlinear systems
We deal with the problem of practical uniform -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results.
Principal solutions and transformations of linear Hamiltonian systems
Sufficient conditions are given which guarantee that the linear transformation converting a given linear Hamiltonian system into another system of the same form transforms principal (antiprincipal) solutions into principal (antiprincipal) solutions.
Propriétés des intégrales des équations différentielles linéaires à coefficients variables
Psi-bounded solutions for linear differential systems with Lebesgue psi-integrable functions on R as right-hand sides.
Quadratic functionals: positivity, oscillation, Rayleigh's principle
In this paper we give a survey on the theory of quadratic functionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh’s principle are demonstrated. Moreover, the main tools form control theory (as e.g. characterization of strong observability), from the calculus of variations (as e.g. field theory and Picone’s identity), and from matrix...
Quadratic functionals with Euler’s equation
Quadratic Integrals of Linear Hamiltonian Systems.
Recent results concerning dynamic equations on time scales.
Reducibility of zero curvature equations.
Reductibilite d'un systeme differentiel lineaire (Reductibility of a Linear Differential System)
Reduction of the modified Poincaré differential equation to Birkhoff matrix form.
Reduction of the modified Poincaré differential equation to Birkhoff matrix form
In this paper the reduction of the modified Poincaré linear differential equation with one -tuple regular singularity to the Birkhoff canonical matrix form is given.