On asymptotic behavior of solutions of second order linear differential equations.
On third-order linear difference equations involving quasi-differences.
On the dynamics of the generalized Emden-Fowler equation.
Disconjugate operators and related differential equations.
On second-order differential equations with nonhomogeneous -Laplacian.
Nonoscillatory half-linear difference equations and recessive solutions.
Positive solutions for singular discrete boundary value problems.
Higher monotonicity properties of special functions: application on Bessel case
The Riccati differential equation with complex-valued coefficients and application to the equation
Monotonicity properties of the linear combination of derivatives of some special functions
Singular quadratic functionals and transformation of linear Hamiltonian systems
On oscillatory solutions of third-order linear differential equations
Oscillation for third-order nonlinear differential equations with deviating argument.
100 let matematiky na Masarykově univerzitě
Článek nabízí stručný přehled témat a osobností, které formovaly rozvoj matematiky na Masarykově univerzitě v Brně od jejího založení v roce 1919. Vývoj vědních oborů sledujeme ve čtyřech obdobích historie univerzity.
A remark on uniqueness criteria for initial value problem
Oscillation of third order differential equation with damping term
We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case and if the corresponding second order differential equation is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.
Singular quadratic functionals of one dependent variable
Singular quadratic functionals of one dependent variable with nonseparated boundary conditions are investigated. Necessary and sufficient conditions for nonnegativity of these functionals are derived using the concept of and . The paper also includes two comparison theorems for coupled points with respect to the various boundary conditions.
Quadratic functionals with a variable singular end point
In this paper we introduce the definition of coupled point with respect to a (scalar) quadratic functional on a noncompact interval. In terms of coupled points we prove necessary (and sufficient) conditions for the nonnegativity of these functionals.
Phases of linear difference equations and symplectic systems
The second order linear difference equation where and , is considered as a special type of symplectic systems. The concept of the phase for symplectic systems is introduced as the discrete analogy of the Borůvka concept of the phase for second order linear differential equations. Oscillation and nonoscillation of (1) and of symplectic systems are investigated in connection with phases and trigonometric systems. Some applications to summation of number series are given, too.
[CDDE 2000. Proceedings of the colloquium on differential and difference equations, Brno, Czech Republic, September 5-8, 2000]. Preface
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