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A remark on the linearization technique in half-linear oscillation theory

Dosly O.

Opuscula Mathematica

2006

Vol. 26, no. 2

305-315

We show that oscillatory properties of the half-linear second order differential equation (r(t)Φ(x'))' + c(t)Φ(x) = 0, Φ(x) = |x|p-2x, p > 1, can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [6], we do not need to distinguish between the cases p ≥ 2 and p ∈ (1, 2]. Our results also improve the oscillation and nonoscillation criteria given in [4].

Hyperbolic transformation and hyperbolic difference systems

Dosly O., Pospisil Z.

Fasciculi Mathematici

2001

Nr 32

25-48

Transformations of symplectic difference systems (mathematical formula) are investigated. It is shown that symplectic systems satisfying certain additional condition can be transformed (using a transformation that preserves oscillation properties of transformed systems) into the so-called hyperbolic difference system. Basic properties of solutions of hyperbolic systems are established.