Picone’s identity for a Finsler p -Laplacian and comparison of nonlinear elliptic equations

Jaroslav Jaroš

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 3, page 535-552
  • ISSN: 0862-7959

Abstract

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In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm H in ℝ n which is continuously differentiable for x ≠ 0 and such that H p is strictly convex for some p > 1 . Two important special cases are the p -Laplacian and the so-called pseudo p -Laplacian. The identity is then used to establish a variety of comparison results concerning nonlinear degenerate elliptic equations which involve such operators. We also get criteria for the nonexistence of positive solutions in exterior domains for such equations by means of comparison with the equation exhibiting a kind of “anisotropic radial symmetry”.

How to cite

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Jaroš, Jaroslav. "Picone’s identity for a Finsler $p$-Laplacian and comparison of nonlinear elliptic equations." Mathematica Bohemica 139.3 (2014): 535-552. <http://eudml.org/doc/261992>.

@article{Jaroš2014,
abstract = {In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm $H$ in $\mathbb \{R\}^n$ which is continuously differentiable for $x \ne 0$ and such that $H^p$ is strictly convex for some $p > 1$. Two important special cases are the $p$-Laplacian and the so-called pseudo $p$-Laplacian. The identity is then used to establish a variety of comparison results concerning nonlinear degenerate elliptic equations which involve such operators. We also get criteria for the nonexistence of positive solutions in exterior domains for such equations by means of comparison with the equation exhibiting a kind of “anisotropic radial symmetry”.},
author = {Jaroš, Jaroslav},
journal = {Mathematica Bohemica},
keywords = {Picone identity; Finsler $p$-Laplacian; Picone identity; Finsler $p$-Laplacian},
language = {eng},
number = {3},
pages = {535-552},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Picone’s identity for a Finsler $p$-Laplacian and comparison of nonlinear elliptic equations},
url = {http://eudml.org/doc/261992},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Jaroš, Jaroslav
TI - Picone’s identity for a Finsler $p$-Laplacian and comparison of nonlinear elliptic equations
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 3
SP - 535
EP - 552
AB - In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm $H$ in $\mathbb {R}^n$ which is continuously differentiable for $x \ne 0$ and such that $H^p$ is strictly convex for some $p > 1$. Two important special cases are the $p$-Laplacian and the so-called pseudo $p$-Laplacian. The identity is then used to establish a variety of comparison results concerning nonlinear degenerate elliptic equations which involve such operators. We also get criteria for the nonexistence of positive solutions in exterior domains for such equations by means of comparison with the equation exhibiting a kind of “anisotropic radial symmetry”.
LA - eng
KW - Picone identity; Finsler $p$-Laplacian; Picone identity; Finsler $p$-Laplacian
UR - http://eudml.org/doc/261992
ER -

References

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