The well-known Picone’s identity plays an important role in the study of qualitative properties of solutions of the second-order linear homogeneous differential equations. It has been recently generalized to the half-linear differential operators
where is a constant, and are real-valued continuous functions on an interval. Using a generalization of Picone’s identity to the linear elliptic operators
a number of authors developed Sturmian theory for second order linear elliptic equations. In this paper, the authors generalized Picone’s identity to the half-linear partial differential operators
where is a constant, and are continuous (continuously differentiable) functions defined in a domain . Then the obtained Picone-type identity is applied to prove Sturmian comparison and oscillation theorems for second-order half-linear degenerate elliptic equations of the form or in an unbounded domain in .