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Picone’s identity; half-linear PDE; $p$-Laplacian; variational technique
The Picone-type identity for the half-linear second order partial differential equation \[ \sum _{i=1}^n\frac{\partial }{\partial x_i} \Phi \bigg (\frac{\partial u}{\partial x_i}\bigg )+c(x)\Phi (u)=0,\quad \Phi (u):=|u|^{p-2}u,\ p>1, \] is established and some applications of this identity are suggested.
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