| Title:
|
Positive solutions of inequality with $p$-Laplacian in exterior domains (English) |
| Author:
|
Mařík, Robert |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
597-604 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper the differential inequality \[\Delta _p u+B(x,u)\le 0,\] where $\Delta _p u=\div (\Vert \nabla u\Vert ^{p-2}\nabla u)$, $p>1$, $B(x,u)\in C(\mathbb{R}^{n}\times \mathbb{R},\mathbb{R})$ 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. (English) |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
oscillation criteria |
| MSC:
|
35B05 |
| MSC:
|
35J60 |
| MSC:
|
35R45 |
| idZBL:
|
Zbl 1074.35505 |
| idMR:
|
MR1942645 |
| DOI:
|
10.21136/MB.2002.133960 |
| . |
| Date available:
|
2009-09-24T22:05:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133960 |
| . |
| Reference:
|
[1] J. I. Díaz: Nonlinear Partial Differential Equations and Free Boundaries.Vol. I, Elliptic Equations, Pitman Publ., London, 1985. MR 0853732 |
| Reference:
|
[2] O. Došlý, R. Mařík: Nonexistence of the positive solutions of partial differential equations with $p$-Laplacian.Acta Math. Hungar. 90 (2001), 89–107. MR 1910321, 10.1023/A:1006739909182 |
| Reference:
|
[3] J. Jaroš, T. Kusano, N. Yoshida: 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. MR 1768900 |
| Reference:
|
[4] R. Mařík: Hartman-Wintner type theorem for PDE with $p$-Laplacian.EJQTDE, Proc. 6th Coll. QTDE, 2000, No. 18, 1–7. MR 1798668 |
| Reference:
|
[5] R. Mařík: Oscillation criteria for PDE with $p$-Laplacian via the Riccati technique.J. Math. Anal. Appl. 248 (2000), 290–308. MR 1772598, 10.1006/jmaa.2000.6901 |
| Reference:
|
[6] E. W. Noussair, C. A. Swanson: Oscillation of semilinear elliptic inequalities by Riccati equation.Can. J. Math. 22 (1980), 908–923. |
| Reference:
|
[7] C. A. Swanson: Semilinear second order ellitpic oscillation.Can. Math. Bull. 22 (1979), 139–157. MR 0537295, 10.4153/CMB-1979-021-0 |
| . |
