| Title:
|
On a class of nonlocal problem involving a critical exponent (English) |
| Author:
|
Ourraoui, Anass |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
23 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
47-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work, by using the Mountain Pass Theorem, we give a result on the existence of solutions concerning a class of nonlocal $p$-Laplacian Dirichlet problems with a critical nonlinearity and small perturbation. (English) |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
Dirichlet problem |
| Keyword:
|
critical exponent. |
| MSC:
|
35J30 |
| MSC:
|
35J60 |
| MSC:
|
35J92 |
| idZBL:
|
Zbl 1355.35063 |
| idMR:
|
MR3394077 |
| . |
| Date available:
|
2015-08-25T13:58:40Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144358 |
| . |
| Reference:
|
[1] Alves, C.O., Corrêa, F.J.S.A., Figueiredo, G.M.: On a class of nonlocal elliptic problems with critical growth.Differential Equation and Applications, 2, 2010, 409-417, Zbl 1198.35281, MR 2731312, 10.7153/dea-02-25 |
| Reference:
|
[2] Azorero, J.G., Alonso, I.P.: Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term.Trans. Amer. Math. Soc., 323, 2, 1991, 877-895, Zbl 0729.35051, MR 1083144, 10.2307/2001562 |
| Reference:
|
[3] Hamidi, A. El, Rakotoson, J.M.: Compactness and quasilinear problems with critical exponents.Differ. Integral Equ., 18, 2005, 1201-1220, Zbl 1212.35113, MR 2174817 |
| Reference:
|
[4] Figueiredo, M. G.: Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument.J. Math. Anal. Appl., 401, 2013, 706-713, Zbl 1307.35110, MR 3018020, 10.1016/j.jmaa.2012.12.053 |
| Reference:
|
[5] Figueiredo, G. M., Santos, Jefferson A.: On a $\Phi $-Kirchhoff multivalued problem with critical growth in an Orlicz-Sobolev space.Asymptotic Analysis, 89, 1, 2014, 151-172, Zbl 1304.35254, MR 3251917 |
| Reference:
|
[6] Fiscella, A., Valdinoci, E.: A critical Kirchhoff type problem involving a nonlocal operator.Nonlinear Anal., 94, 2014, 156-170, Zbl 1283.35156, MR 3120682, 10.1016/j.na.2013.08.011 |
| Reference:
|
[7] Fukagai, N., Narukawa, K.: Positive solutions of quasilinear elliptic equations with critical Orlicz–Sobolev nonlinearity on RN.Funkciallaj Ekvacioj, 49, 1981, 235-267, MR 2271234, 10.1619/fesi.49.235 |
| Reference:
|
[8] Lions, P. L.: The concentraction-compactness principle in the calculus of virations. The limit case, Part 1.Rev Mat Iberoamericana, 1, 1985, 145-201, MR 0834360, 10.4171/RMI/6 |
| Reference:
|
[9] Ourraoui, A.: On a $p$-Kirchhoff problem involving a critical nonlinearity.C. R. Acad. Sci. Paris, 352, 2014, 295-298, Zbl 1298.35096, MR 3186916, 10.1016/j.crma.2014.01.015 |
| Reference:
|
[10] Pucci, P.: Geometric description of the mountain pass critical points.Contemporary Mathematicians, 2, 2014, 469-471. |
| Reference:
|
[11] Pucci, P., Saldi, S.: Critical stationary Kirchhoff equations in $R^N$ involving nonlocal operators.Rev. Mat. Iberoam., 2014, MR 3470662 |
| Reference:
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| . |
