Half-linear dynamic equations with mixed derivatives
Texas State University-San Marcos, Department of Mathematics
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.
Time scale, Half-linear dynamic equations, Mixed derivatives, Picone's identity, Roundabout theorem
Dosly, O., & Marek, D. (2005). Half-linear dynamic equations with mixed derivatives. <i>Electronic Journal of Differential Equations, 2005</i>(90), pp. 1-18.