| Title:
|
Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach (English) |
| Author:
|
Drábek, Pavel |
| Author:
|
Moudan, Zakaria |
| Author:
|
Touzani, Abdelfettah |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
421-431 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The nonlinear eigenvalue problem for p-Laplacian $$ \cases - \operatorname{div} (a(x) |\nabla u|^{p-2} \nabla u) = \lambda g (x) |u|^{p-2} u \text{ in } \Bbb R^N, \ u >0 \text{ in } \Bbb R^N, \mathop{\lim}\limits_{|x|\to \infty} u(x) = 0, \endcases $$ is considered. We assume that $1 < p < N$ and that $g$ is indefinite weight function. The existence and $C^{1, \alpha}$-regularity of the weak solution is proved. (English) |
| Keyword:
|
eigenvalue |
| Keyword:
|
the p-Laplacian |
| Keyword:
|
indefinite weight |
| Keyword:
|
regularity |
| MSC:
|
35J65 |
| MSC:
|
35J70 |
| MSC:
|
35P30 |
| MSC:
|
49J40 |
| MSC:
|
49R50 |
| idZBL:
|
Zbl 0940.35150 |
| idMR:
|
MR1485065 |
| . |
| Date available:
|
2009-01-08T18:35:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118942 |
| . |
| Reference:
|
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| Reference:
|
[2] Allegretto W., Huang Y.X.: Eigenvalues of the indefinite weight p-Laplacian in weighted spaces.Funkc. Ekvac. 38 (1995), 233-242. Zbl 0922.35114, MR 1356326 |
| Reference:
|
[3] Drábek P.: Nonlinear eigenvalue for p-Laplacian in $\Bbb R^N$.Math. Nach 173 (1995), 131-139. MR 1336957 |
| Reference:
|
[4] Drábek, Huang Y.X.: Bifurcation problems for the p-Laplacian in $\Bbb R^N$.to appear in Trans. of AMS. |
| Reference:
|
[5] Fleckinger J., Manasevich R.F., Stavrakakis N.M., de Thelin F.: Principal eigenvalues for some quasilinear elliptic equations on $\Bbb R^N$.preprint. |
| Reference:
|
[6] Huang Y.X.: Eigenvalues of the p-Laplacian in $\Bbb R^N$ with indefinite weight.Comment. Math. Univ. Carolinae 36 (1995), 519-527. MR 1364493 |
| Reference:
|
[7] Lindqvist P.: On the equation ${div} (|\nabla u|^{p-2} \nabla u) + \lambda |u|^{p-2} u = 0$.Proc. Amer. Math. Society 109 (1990), 157-164. Zbl 0714.35029, MR 1007505 |
| Reference:
|
[8] Serin J.: Local behavior of solutions of quasilinear equations.Acta Math. 111 (1964), 247-302. MR 0170096 |
| Reference:
|
[9] Tolkdorf P.: Regularity for a more general class of quasilinear elliptic equations.J. Diff. Equations 51 (1984), 126-150. MR 0727034 |
| Reference:
|
[10] Trudinger N.S.: On Harnack type inequalities and their applications to quasilinear elliptic equations.Comm. Pure. Appl. Math. 20 (1967), 721-747. MR 0226198 |
| . |
