The Picone identity for a class of partial differential equations

Ondřej Došlý

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 4, page 581-589
  • ISSN: 0862-7959

Abstract

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The Picone-type identity for the half-linear second order partial differential equation ∑ i = 1 n ∂ ∂ x i Φ ∂ u ∂ x i + c ( x ) Φ ( u ) = 0 , Φ ( u ) : = | u | p - 2 u , p > 1 , is established and some applications of this identity are suggested.

How to cite

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Došlý, Ondřej. "The Picone identity for a class of partial differential equations." Mathematica Bohemica 127.4 (2002): 581-589. <http://eudml.org/doc/249052>.

@article{Došlý2002,
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.},
author = {Došlý, Ondřej},
journal = {Mathematica Bohemica},
keywords = {Picone’s identity; half-linear PDE; $p$-Laplacian; variational technique; Picone's identity; half-linear PDE; -Laplacian; variational technique},
language = {eng},
number = {4},
pages = {581-589},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Picone identity for a class of partial differential equations},
url = {http://eudml.org/doc/249052},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Došlý, Ondřej
TI - The Picone identity for a class of partial differential equations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 4
SP - 581
EP - 589
AB - 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.
LA - eng
KW - Picone’s identity; half-linear PDE; $p$-Laplacian; variational technique; Picone's identity; half-linear PDE; -Laplacian; variational technique
UR - http://eudml.org/doc/249052
ER -

References

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