Interval criteria for oscillation of second-order half-linear differential equations.
The authors consider the second-order half-linear differential equation \[ [r(t)| x'|^{\alpha- 1} x']'+ q(t)| x|^{\alpha-1} x=0 \] with \(\alpha> 0\). By employing the techniques used by Q. Kong for the linear case, they establish interval criteria for oscillation, i.e., criteria for oscillation based on the information of the equation on a sequence on intervals rather than on the half-line \([0,\infty)\). Several follow-up sufficient conditions are obtained. A couple of examples are also given for demonstration. Here, it should be pointed out that due to lack of research sources, the authors did not know that similar work has been done by \textit{Q. Kong} [Fields Inst. Commun. 21, 317--323 (1999; Zbl 0924.34025)]. The present work should be regarded as a generalization of the above Kong's work using a more general Riccati variable.
scientific article; zbMATH DE number 2056507