Positive solutions of inequality with p -Laplacian in exterior domains

Robert Mařík

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 4, page 597-604
  • ISSN: 0862-7959

Abstract

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In the paper the differential inequality Δ p u + B ( x , u ) 0 , where Δ p u = div ( u p - 2 u ) , p > 1 , B ( x , u ) C ( n × , ) is studied. Sufficient conditions on the function B ( x , u ) are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.

How to cite

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Mařík, Robert. "Positive solutions of inequality with $p$-Laplacian in exterior domains." Mathematica Bohemica 127.4 (2002): 597-604. <http://eudml.org/doc/249025>.

@article{Mařík2002,
abstract = {In the paper the differential inequality \[\Delta \_p u+B(x,u)\le 0,\] where $\Delta _p u=\operatorname\{div\}(\Vert \nabla u\Vert ^\{p-2\}\nabla u)$, $p>1$, $B(x,u)\in C(\mathbb \{R\}^\{n\}\times \mathbb \{R\},\mathbb \{R\})$ is studied. Sufficient conditions on the function $B(x,u)$ are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.},
author = {Mařík, Robert},
journal = {Mathematica Bohemica},
keywords = {$p$-Laplacian; oscillation criteria; -Laplacian; oscillation criteria},
language = {eng},
number = {4},
pages = {597-604},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive solutions of inequality with $p$-Laplacian in exterior domains},
url = {http://eudml.org/doc/249025},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Mařík, Robert
TI - Positive solutions of inequality with $p$-Laplacian in exterior domains
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 4
SP - 597
EP - 604
AB - In the paper the differential inequality \[\Delta _p u+B(x,u)\le 0,\] where $\Delta _p u=\operatorname{div}(\Vert \nabla u\Vert ^{p-2}\nabla u)$, $p>1$, $B(x,u)\in C(\mathbb {R}^{n}\times \mathbb {R},\mathbb {R})$ is studied. Sufficient conditions on the function $B(x,u)$ are established, which guarantee nonexistence of an eventually positive solution. The generalized Riccati transformation is the main tool.
LA - eng
KW - $p$-Laplacian; oscillation criteria; -Laplacian; oscillation criteria
UR - http://eudml.org/doc/249025
ER -

References

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  1. Nonlinear Partial Differential Equations and Free Boundaries, Vol. I, Elliptic Equations, Pitman Publ., London, 1985. (1985) MR0853732
  2. 10.1023/A:1006739909182, Acta Math. Hungar. 90 (2001), 89–107. (2001) MR1910321DOI10.1023/A:1006739909182
  3. A Picone type identity and Sturmian comparison and oscillation theorems for a class of half-linear partial differential equation of second order, Nonlinear Anal. Theory Methods Appl. 40 (2000), 381–395. (2000) MR1768900
  4. Hartman-Wintner type theorem for PDE with p -Laplacian, EJQTDE, Proc. 6th Coll. QTDE, 2000, No. 18, 1–7. MR1798668
  5. 10.1006/jmaa.2000.6901, J. Math. Anal. Appl. 248 (2000), 290–308. (2000) MR1772598DOI10.1006/jmaa.2000.6901
  6. Oscillation of semilinear elliptic inequalities by Riccati equation, Can. J. Math. 22 (1980), 908–923. (1980) 
  7. 10.4153/CMB-1979-021-0, Can. Math. Bull. 22 (1979), 139–157. (1979) MR0537295DOI10.4153/CMB-1979-021-0

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