| Title:
|
Multiplicity of positive solutions for second order quasilinear equations (English) |
| Author:
|
Bouafia, Dahmane |
| Author:
|
Moussaoui, Toufik |
| Author:
|
O'Regan, Donal |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
93-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss the existence and multiplicity of positive solutions for a class of second order quasilinear equations. To obtain our results we will use the Ekeland variational principle and the Mountain Pass Theorem. (English) |
| Keyword:
|
critical point |
| Keyword:
|
Ekeland variational principle |
| Keyword:
|
Mountain Pass Theorem |
| Keyword:
|
Palais-Smale condition |
| Keyword:
|
positive solution |
| MSC:
|
30E25 |
| MSC:
|
35A15 |
| MSC:
|
35B38 |
| MSC:
|
49K35 |
| MSC:
|
58E30 |
| idZBL:
|
07217183 |
| idMR:
|
MR4088696 |
| DOI:
|
10.21136/MB.2019.0051-18 |
| . |
| Date available:
|
2020-03-12T08:21:29Z |
| Last updated:
|
2020-11-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148067 |
| . |
| Reference:
|
[1] Alves, C. O.: Multiple positive solutions for equations involving critical Sobolev exponent in $\mathbb{R}^{N}$.Electron. J. Differ. Equ. 13 (1997), Paper No. 13, 10 pages. Zbl 0886.35056, MR 1461975 |
| Reference:
|
[2] Bouafia, D., Moussaoui, T., O'Regan, D.: Existence of solutions for a second order problem on the half-line via Ekeland's variational principle.Discuss. Math. Differ. Incl. Control Optim. 36 (2016), 131-140. MR 3644383, 10.7151/dmdico.1187 |
| Reference:
|
[3] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations.Universitext. Springer, New York (2010). Zbl 1220.46002, MR 2759829, 10.1007/978-0-387-70914-7 |
| Reference:
|
[4] Ekeland, I.: On the variational principle.J. Math. Anal. Appl. 47 (1974), 324-353. Zbl 0286.49015, MR 0346619, 10.1016/0022-247X(74)90025-0 |
| Reference:
|
[5] Frites, O., Moussaoui, T., O'Regan, D.: Existence of solutions via variational methods for a problem with nonlinear boundary conditions on the half-line.Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 22 (2015), 395-407. Zbl 1333.34029, MR 3423280 |
| Reference:
|
[6] Jabri, Y.: The Mountain Pass Theorem. Variants, Generalizations and Some Applications.Encyclopedia of Mathematics and Its Applications 95. Cambridge University Press, Cambridge (2003). Zbl 1036.49001, MR 2012778, 10.1017/CBO9780511546655 |
| Reference:
|
[7] Willem, M.: Minimax Theorems.Progress in Nonlinear Differential Equations and Their Applications 24. Birkhäuser, Boston (1996). Zbl 0856.49001, MR 1400007, 10.1007/978-1-4612-4146-1 |
| . |
