Nonoscillation theory for second order half-linear differential equations in the framework of regular variation
The authors study regularity properties implying nonoscillation of the solutions of the half-linear equation \[ (| y'|^{\alpha- 1}y')'+ q(t)| y|^{\alpha- 1}y= 0 \] with \(\alpha> 0\) and \(q\) positive and continuous on the half-axis \(t\geq 0\). Some necessary and sufficient conditions for the existence of such solutions are presented. The results generalize corresponding ones for the linear equation (when \(\alpha= 1\)) as proved in [\textit{V. Marić}, Regular variation and differential equations. Lecture Notes in Mathematics 1726. Berlin: Springer-Verlag (2000; Zbl 0946.34001)].
scientific article; zbMATH DE number 2002348