Displaying similar documents to “Hardy inequality on time scales and its application to half-linear dynamic equations.”

A role of the coefficient of the differential term in qualitative theory of half-linear equations

Pavel Řehák (2010)

Mathematica Bohemica

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The aim of this contribution is to study the role of the coefficient r in the qualitative theory of the equation ( r ( t ) Φ ( y Δ ) ) Δ + p ( t ) Φ ( y σ ) = 0 , where Φ ( u ) = | u | α - 1 sgn u with α > 1 . We discuss sign and smoothness conditions posed on r , (non)availability of some transformations, and mainly we show how the behavior of r , 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...

Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

Özkan Öztürk, Elvan Akın (2016)

Nonautonomous Dynamical Systems

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We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.

Oscillatory properties of second order half-linear difference equations

Pavel Řehák (2001)

Czechoslovak Mathematical Journal

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We study oscillatory properties of the second order half-linear difference equation Δ ( r k | Δ y k | α - 2 Δ y k ) - p k | y k + 1 | α - 2 y k + 1 = 0 , α > 1 . ( HL ) It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation Δ ( r k Δ y k ) - p k y k + 1 = 0 . We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.