Half-linear dynamic equations with mixed derivatives
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We 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.
CitationDosly, O., & Marek, D. (2005). Half-linear dynamic equations with mixed derivatives. Electronic Journal of Differential Equations, 2005(90), pp. 1-18.
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