On transformations of self-adjoint linear differential systems and their reciprocals
Sixty years of professor František Neuman
Sixty years of professor František Neuman
Representation of solutions of general linear differential systems of the second order
A remark on polyconvex envelopes of radially symmetric functions in dimension
We study polyconvex envelopes of a class of functions related to the function of Kohn and Strang introduced in . We present an example of a function of this class for which the polyconvex envelope may be computed explicitly and we also point out some general features of the problem.
The basic properties of phase matrices of linear differential systems
Riccati matrix differential equation and classification of disconjugate differential systems
On transformations of self-adjoint linear differential systems
Transformations of linear Hamiltonian systems preserving oscillatory behaviour
Phase matrix of linear differential systems
Second phase matrix of differential systems
Oscillatory properties of fourth order Sturm-Liouville differential equations
On some properties of trigonometric matrices
Solutions of Riemann–Weber type half-linear differential equation
We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.
Oscillation Theory of Linear Difference Equations
Generalized reciprocity for self-adjoint linear differential equations
Let , be an -th order differential operator, be its adjoint and be positive functions. It is proved that the self-adjoint equation is nonoscillatory at if and only if the equation is nonoscillatory at . Using this result a new necessary condition for property BD of the self-adjoint differential operators with middle terms is obtained.
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.
On conjugate points of solutions of non-selfadjoint differential systems
Methods of oscillation theory of half-linear second order differential equations
In this paper we investigate oscillatory properties of the second order half-linear equation Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.
On some problems in the oscillation theory of self-adjoint linear differential equations
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