Contribution to the monotonicity of the sequence of zero points of integrals of the differential equation with regard to the basis
Controllability and observability of time-invariant linear dynamic systems
In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.
Coordinate description of analytic relations
In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.
Coppel-Conti sets of linear systems.
Covariant constructions in the theory of linear differential equations
Decomposing a 4th order linear differential equation as a symmetric product
Let L(y) = 0 be a linear differential equation with rational functions as coefficients. To solve L(y) = 0 it is very helpful if the problem could be reduced to solving linear differential equations of lower order. One way is to compute a factorization of L, if L is reducible. Another way is to see if an operator L of order greater than 2 is a symmetric power of a second order operator. Maple contains implementations for both of these. The next step would be to see if L is a symmetric product of...
Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation...
Der verallgemeinerte Ljapunovsche Oszillationssatz
Derivative of the norm of a linear mapping and its application to differential equations
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
Die asymptotischen Formeln für die Lösungen der kanonischen Differentialgleichung 3. Ordnung
Die Form der Integrale der linearen Differentialgleichungen.
Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten
Die Kummerschen Transformationen in Räumen mit abgeschlossenen Phasen. Teil A: Allgemeine Eigenschaften
Die Kummerschen Transformationen in Räumen mit abgeschlossenen Phasen. Teil B: Transformationen in Räumen der gegeben Klasse
Die möglichen Wachstumsordnungen der Lösungen von linearen Differentialgleichungen.
Die Transformationsfunktion für eine Differentialgleichung zweiter Ordnung
Diferenciální rovnice v ČSR v letech 1945-1985
Different types of solvability conditions for differential operators.
Differential and Integral Equations [Book]
Differential equations associated with generalized Bell polynomials and their zeros
In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.