MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 581-589 (2002)

The Picone identity for a class of partial differential equations

Ondrej Dosly

Ondrej Dosly, Mathematical Institute, AS CR, Zizkova 22, CZ-616 62 Brno, e-mail:

Abstract: 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.

Keywords: Picone's identity, half-linear PDE, $p$-Laplacian, variational technique

Classification (MSC2000): 35J20

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