| Title:
|
Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities (English) |
| Author:
|
Anello, Giovanni |
| Author:
|
Rao, Giuseppe |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
485-491 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p>1$, $q>p$, $\lambda >0$ and $s\in ]1,p[$. We study, for $s\rightarrow p^-$, the behavior of positive solutions of the problem $-\Delta_p u = \lambda u^{s-1}+u^{q-1}$ in $\Omega$, $u_{\mid\partial \Omega}=0$. In particular, we give a positive answer to an open question formulated in a recent paper of the first author. (English) |
| Keyword:
|
elliptic boundary value problems |
| Keyword:
|
positive solutions |
| Keyword:
|
variational methods |
| Keyword:
|
asymptotic behavior |
| Keyword:
|
combined nonlinearities |
| MSC:
|
35J20 |
| MSC:
|
35J25 |
| MSC:
|
35J92 |
| idZBL:
|
Zbl 06373979 |
| idMR:
|
MR3125071 |
| . |
| Date available:
|
2013-10-01T21:11:30Z |
| Last updated:
|
2016-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143471 |
| . |
| Reference:
|
[1] Anello G.: On the Dirichlet problem involving the equation $-\Delta_p u=\lambda u^{s-1}$.Nonlinear Anal. 70 (2009), 2060–2066. MR 2492142 |
| Reference:
|
[2] Anello G.: Asymptotic behavior of positive solutions of a Dirichlet problem involving combined nonlinearities.Monatsh. Math. 162 (2011), 1–18. Zbl 1206.35135, MR 2747340, 10.1007/s00605-010-0189-9 |
| Reference:
|
[3] Boccardo L., Escobedo M., Peral I.: A Dirichlet problem involving critical exponent.Nonlinear Anal. 24 (1995), no. 11, 1639–1648. MR 1328589, 10.1016/0362-546X(94)E0054-K |
| Reference:
|
[4] Gedda M., Veron L.: Quasilinear elliptic equations involving critical Sobolev exponent.Nonlinear Anal. 13 (1989), no. 8, 879–902. MR 1009077, 10.1016/0362-546X(89)90020-5 |
| Reference:
|
[5] Il'yasov Y.: On nonlocal existence results for elliptic equations with convex concave nonlinearities.Nonlinear Anal. 61 (2005), 211–236. Zbl 1190.35112, MR 2122250, 10.1016/j.na.2004.10.022 |
| Reference:
|
[6] Liebermann G.M.: Boundary regularity for solutions of degenerate elliptic equations.Nonlinear Anal. 12 (1988), no. 11, 1203–1219. MR 0969499, 10.1016/0362-546X(88)90053-3 |
| Reference:
|
[7] Moser J.: A new proof of De Giorgi's Theorem concerning the regularity problem for elliptic differential equations.Comm. Pure Appl. Math. 13 (1960), 457–478. Zbl 0111.09301, MR 0170091, 10.1002/cpa.3160130308 |
| . |
