Peculiarities in power type comparison results for half-linear dynamic equations
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Rocky Mountain Journal of Mathematics |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | half-linear dynamic equation; time scale; comparison theorem |
| Description | We look for conditions guaranteeing that oscillatory properties of a half-linear dynamic equation are preserved when the power in the nonlinearities is changed. In particular, we discuss discrepancies (which indeed occur) between the results on different time scales. We provide an example showing an optimality of one of the assumptions. We also present one generalization of a standard Sturm-Picone type comparison theorem and give an important note on the smoothness condition for the coefficient in the leading term which concerns general theory of second order dynamic equations. Many of our observations are new also in the differential and difference equations cases. |
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