| Title:
|
Infinitely many solutions of a second-order $p$-Laplacian problem with impulsive condition (English) |
| Author:
|
Wang, Libo |
| Author:
|
Ge, Weigao |
| Author:
|
Pei, Minghe |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
5 |
| Year:
|
2010 |
| Pages:
|
405-418 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a $p$-Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the $p$-Laplacian impulsive problem. (English) |
| Keyword:
|
critical point theory |
| Keyword:
|
lower and upper solutions |
| Keyword:
|
impulsive |
| Keyword:
|
$p$-Laplacian |
| MSC:
|
34A45 |
| MSC:
|
34B18 |
| MSC:
|
34B37 |
| MSC:
|
47H15 |
| MSC:
|
47J30 |
| MSC:
|
58E05 |
| idZBL:
|
Zbl 1224.34091 |
| idMR:
|
MR2737720 |
| DOI:
|
10.1007/s10492-010-0015-7 |
| . |
| Date available:
|
2010-11-24T08:14:58Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140710 |
| . |
| Reference:
|
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| Reference:
|
[2] Cîrstea, F., Motreanu, D., Rădulescu, V.: Weak solutions of quasilinear problems with nonlinear boundary condition.Nonlinear Anal., Theory Methods Appl. 43 (2001), 623-636. MR 1804861, 10.1016/S0362-546X(99)00224-2 |
| Reference:
|
[3] Costa, D. G., Magalhães, C. A.: Existence results for perturbations of the $p$-Laplacian.Nonlinear Anal., Theory Methods Appl. 24 (1995), 409-418. MR 1312776, 10.1016/0362-546X(94)E0046-J |
| Reference:
|
[4] Coster, C. De, Habets, P.: Two-point Boundary Value Problems. Lower and Upper Solutions.Elsevier Amsterdam (2006). MR 2225284 |
| Reference:
|
[5] Amrouss, A. R. El, Moussaoui, M.: Minimax principle for critical point theory in applications to quasilinear boundary value problems.Electron. J. Differ. Equ. 18 (2000), 1-9. MR 1744087 |
| Reference:
|
[6] Guo, Y., Liu, J.: Solutions of $p$-sublinear $p$-Laplacian equation via Morse theory.J. Lond. Math. Soc. 72 (2005), 632-644. Zbl 1161.35405, MR 2190329, 10.1112/S0024610705006952 |
| Reference:
|
[7] Nieto, J. J., O'Regan, D.: Variational approach to impulsive differential equation.Nonlinear Anal., Real World Appl. 10 (2009), 680-690. MR 2474254 |
| Reference:
|
[8] Omari, P., Zanolin, F.: An elliptic problem with arbitrarily small positive solutions.Electron. J. Differ. Equ., Conf. 05 (2000), 301-308. Zbl 0959.35059, MR 1799060 |
| . |
