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...

New equivalent conditions for Hardy-type inequalities

Alois Kufner, Komil Kuliev, Gulchehra Kulieva, Mohlaroyim Eshimova (2024)

Mathematica Bohemica

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We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial in the study of oscillation and non-oscillation properties of differential equation solutions, as well as spectral properties.

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.