| Title:
|
Multiple positive solutions to multipoint one-dimensional $p$-Laplacian boundary value problem with impulsive effects (English) |
| Author:
|
Tian, Yuansheng |
| Author:
|
Chen, Anping |
| Author:
|
Ge, Weigao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
127-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, using a fixed point theorem on a convex cone, we consider the existence of positive solutions to the multipoint one-dimensional $p$-Laplacian boundary value problem with impulsive effects, and obtain multiplicity results for positive solutions. (English) |
| Keyword:
|
$p$-Laplacian operator |
| Keyword:
|
boundary value problem |
| Keyword:
|
impulsive differential equations |
| Keyword:
|
fixed-point theorem |
| Keyword:
|
positive solutions |
| MSC:
|
34B15 |
| MSC:
|
34B18 |
| MSC:
|
34B37 |
| idZBL:
|
Zbl 1224.34090 |
| idMR:
|
MR2782764 |
| DOI:
|
10.1007/s10587-011-0002-5 |
| . |
| Date available:
|
2011-05-23T12:36:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141523 |
| . |
| Reference:
|
[1] Bai, Z., Ge, W.: Existence of three positive solutions for some second-order boundary value problems.Comput. Math. Appl. 48 (2004), 699-707. Zbl 1066.34019, MR 2105244, 10.1016/j.camwa.2004.03.002 |
| Reference:
|
[2] Chen, L., Sun, J.: Nonlinear boundary value problem of first order impulsive functional differential equations.J. Math. Anal. Appl. 318 (2006), 726-741. Zbl 1102.34052, MR 2215181, 10.1016/j.jmaa.2005.08.012 |
| Reference:
|
[3] Ding, W., Han, M.: Periodic boundary value problem for the second order impulsive functional differential equations.Appl. Math. Comput. 155 (2004), 709-726. Zbl 1102.34324, MR 2078208, 10.1016/S0096-3003(03)00811-7 |
| Reference:
|
[4] Kaufmann, E. R., Kosmatov, N., Raffoul, Y. N.: A second-order boundary value problem with impulsive effects on an unbounded domain.Nonlinear Anal., Theory Methods Appl. 69 (2008), 2924-2929. Zbl 1159.34023, MR 2452102 |
| Reference:
|
[5] Lin, X., Jiang, D.: Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations.J. Math. Anal. Appl. 321 (2006), 501-514. Zbl 1103.34015, MR 2241134, 10.1016/j.jmaa.2005.07.076 |
| Reference:
|
[6] Lee, Y.-H., Liu, X.: Study of singular boundary value problems for second order impulsive differential equations.J. Math. Anal. Appl. 331 (2007), 159-176. Zbl 1120.34018, MR 2305995, 10.1016/j.jmaa.2006.07.106 |
| Reference:
|
[7] Lee, E. K., Lee, Y.-H.: Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equation.Appl. Math. Comput. 158 (2004), 745-759. MR 2095700, 10.1016/j.amc.2003.10.013 |
| Reference:
|
[8] Rachůnková, I., Tomeček, J.: Singular Dirichlet problem for ordinary differential equation with impulses.Nonlinear Anal., Theory Methods Appl. 65 (2006), 210-229. MR 2226265, 10.1016/j.na.2005.09.016 |
| Reference:
|
[9] Rachůnková, I., Tvrdý, M.: Second-order periodic problem with $\varphi $-Laplacian and impulses.Nonlinear Anal., Theory Methods Appl. 63 (2005), 257-266. 10.1016/j.na.2004.09.017 |
| Reference:
|
[10] Su, H., Wei, Z., Wang, B.: The existence of positive solutions for a nonlinear four-point singular boundary value problem with a $p$-Laplacian operator.Nonlinear Anal., Theory Methods Appl. 66 (2007), 2204-2217. Zbl 1126.34017, MR 2311023 |
| Reference:
|
[11] Shen, J., Wang, W.: Impulsive boundary value problems with nonlinear boundary conditions.Nonlinear Anal., Theory Methods Appl. 69 (2008), 4055-4062. Zbl 1171.34309, MR 2463353, 10.1016/j.na.2007.10.036 |
| Reference:
|
[12] Tian, Y., Jiang, D., Ge, W.: Multiple positive solutions of periodic boundary value problems for second order impulsive differential equations.Appl. Math. Comput. 200 (2008), 123-132. Zbl 1156.34019, MR 2421630, 10.1016/j.amc.2007.10.052 |
| Reference:
|
[13] Wang, Y., Hou, C.: Existence of multiple positive solutions for one dimensional $p$-Laplacian.J. Math. Anal. Appl. 315 (2006), 144-153. Zbl 1098.34017, MR 2196536, 10.1016/j.jmaa.2005.09.085 |
| Reference:
|
[14] Zhang, X., Ge, W.: Impulsive boundary value problems involving the one-dimensional $p$-Laplacian.Nonlinear Anal., Theory Methods Appl. 70 (2009), 1692-1701. Zbl 1183.34038, MR 2483590, 10.1016/j.na.2008.02.052 |
| . |
