Asymptotic behavior of solutions to half-linear -difference equations.
Half-linear discrete oscillation theory.
Hardy inequality on time scales and its application to half-linear dynamic equations.
How the constants in Hille-Nehari theorems depend on time scales.
On certain comparison theorems for half-linear dynamic equations on time scales.
A Riccati technique for proving oscillation of a half-linear equation.
Regularly varying solutions of second-order difference equations with arbitrary sign coefficient.
Zero convergent solutions for a class of -Laplacian systems
Nonoscillatory solutions for nonlinear discrete systems
Boundary value problems for functional difference equations on infinite intervals.
Regulární variace: od škálové invariance ke konvergenčním testům
Článek se snaží přiblížit některé aspekty teorie regulární variace. Jde o pojem z klasické analýzy, který má bohatou historii a četné aplikace v teorii pravděpodobnosti, teorii čísel, integrálních transformacích, komplexní analýze, diferenciálních rovnicích, teorii her či teorii grafů. Regulárně měnící se funkce mají souvislost s mnoha matematickými pojmy, včetně škálové invariance, kterou náš výklad začíná, či konvergenčními testy pro nekonečné řady, kterými náš výklad končí. V průběhu výkladu...
Oscillatory properties of second order half-linear difference equations
We study oscillatory properties of the second order half-linear difference equation It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.
A role of the coefficient of the differential term in qualitative theory of half-linear equations
The aim of this contribution is to study the role of the coefficient in the qualitative theory of the equation , where with . We discuss sign and smoothness conditions posed on , (non)availability of some transformations, and mainly we show how the behavior of , along with the behavior of the graininess of the time scale, affect some comparison results and (non)oscillation criteria. At the same time we provide a survey of recent results acquired by sophisticated modifications of the Riccati...
Second order linear -difference equations: nonoscillation and asymptotics
The paper can be understood as a completion of the -Karamata theory along with a related discussion on the asymptotic behavior of solutions to the linear -difference equations. The -Karamata theory was recently introduced as the theory of regularly varying like functions on the lattice with . In addition to recalling the existing concepts of -regular variation and -rapid variation we introduce -regularly bounded functions and prove many related properties. The -Karamata theory is then...
Conjugacy criteria for second order linear difference equations
We establish conditions which guarantee that the second order difference equation possesses a nontrivial solution with at least two generalized zero points in a given discrete interval
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