A Picone identity for half-linear elliptic equations and its applications to oscillation theory

Abstract

A Picone identity is established for a class of half-linear elliptic operators, and Sturmian comparison and oscillation results are derived on the basis of the Picone identity. Wirtinger inequalities and Riccati inequalities are also obtained as corollaries of the Picone identity, and a new class of half-linear elliptic equations is introduced.