Dosly, OndrejMarek, Daniel2021-06-012021-06-012005-08-15Dosly, O., & Marek, D. (2005). Half-linear dynamic equations with mixed derivatives. <i>Electronic Journal of Differential Equations, 2005</i>(90), pp. 1-18.1072-6691https://hdl.handle.net/10877/13691We investigate oscillatory properties of the second order half-linear dynamic equation on a time scale with mixed derivatives (r(t)Φ(x∆))∇ + c(t)Φ(x) = 0, Φ(x) = |x|p-2x, p > 1. In particular, we establish the Roundabout theorem which relates oscillatory properties of this equation to the solvability of the associated Riccati-type dynamic equation and to the positivity of the corresponding energy functional. This result is then used to prove (non)oscillation criteria for the above equation.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalTime scaleHalf-linear dynamic equationsMixed derivativesPicone's identityRoundabout theoremArticle