| Title:
|
On general solvability properties of $p$-Lapalacian-like equations (English) |
| Author:
|
Drábek, Pavel |
| Author:
|
Simader, Christian G. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
103-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation \[ -\Delta _p u = f \ \text{in} \ \Omega , \] where $\Omega $ is a very general domain in $\mathbb{R}^N$, including the case $\Omega = \mathbb{R}^N$. (English) |
| Keyword:
|
quasilinear elliptic equations |
| Keyword:
|
weak solutions |
| Keyword:
|
solvability |
| MSC:
|
35B40 |
| MSC:
|
35J15 |
| MSC:
|
35J20 |
| MSC:
|
35J60 |
| idZBL:
|
Zbl 1030.35058 |
| idMR:
|
MR1895250 |
| DOI:
|
10.21136/MB.2002.133987 |
| . |
| Date available:
|
2009-09-24T21:58:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133987 |
| . |
| Reference:
|
[1] P. Drábek: Solvability and Bifurcations of Nonlinear Equations.Pitman Research Notes in Mathematics Series 264, Longman, 1992. MR 1175397 |
| Reference:
|
[2] P. Drábek, A. Kufner, F. Nicolosi: Quasilinear Elliptic Equations with Degenerations and Singularities, de Gruyter Series in Nonlinear Analysis and Applications 5.Walter de Gruyter, Berlin, 1997. MR 1460729 |
| Reference:
|
[3] P. Drábek, C. G. Simader: Nonlinear eigenvalue problem for quasilinear equations in unbounded domains.Math. Nachrichten 203 (1999), 5–30. MR 1698637, 10.1002/mana.1999.3212030102 |
| Reference:
|
[4] S. Fučík, A. Kufner: Nonlinear Differential Equations.Elsevier, Amsterdam, 1980. MR 0558764 |
| Reference:
|
[5] S. Fučík, J. Nečas, J. Souček, V. Souček: Spectral Analysis of Nonlinear Operators.Lecture Notes in Mathematics 346, Springer, Berlin, 1973. MR 0467421 |
| Reference:
|
[6] D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order.Springer, Berlin, 1977. MR 0473443 |
| Reference:
|
[7] V. Goldshtein, M. Troyanov: Sur la non résolubilité du $p$-laplacien C.R.Acad. Sci. Paris, t. 326, Sér. I (1998), 1185–1187. MR 1650266 |
| Reference:
|
[8] A. Kufner, O. John, S. Fučík: Function Spaces.Academia, Praha, 1977. MR 0482102 |
| Reference:
|
[9] J. Naumann, C. G.Simader: A second look on definition and equivalent norms of Sobolev spaces.Math. Bohem. 124 (1999), 315–328. Zbl 0941.46019, MR 1780700 |
| Reference:
|
[10] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[11] C. G. Simader: Sobolev’s original definition of his spaces revisited and a comparison with nowadays definition.Le Matematiche 54 (1999), 149–178. Zbl 0947.46022, MR 1749828 |
| Reference:
|
[12] C. G. Simader, H. Sohr: The Dirichlet Problem for the Laplacian in Bounded and Unbounded Domains.Pitman Research Notes in Mathematics Series 360, Addison Wesley Longman, 1996. MR 1454361 |
| . |
