Riccati technique for oscillation of half-linear/Emden-Fowler neutral dynamic equations

Abstract

By using the Riccati technique, which reduces the higher order dynamic equations to a Riccati dynamic inequality, we will establish some new sufficient conditions for the oscillation of half-linear/Emden-Fowler neutral dynamic equation of the form \[ (r(\varrho)((\mathbf{\mathbf{x}}(\varrho)+p(\varrho)\mathbf{x}(\tau (\varrho)))^{\Delta })^{\gamma })^{\Delta }+q(\varrho)\mathbf{x}^{a }(\delta (\varrho))+v(\varrho)\mathbf{x}^{\beta }(\eta (\varrho))=0, \] on a time scale \(\mathcal{T}\), where \(\gamma \), \(a \), and \(\beta \) are quotients of odd positive integers. An example with particular equation is constructed in consistent to the above equation and oscillation criteria are established for its solution.