| Title:
|
Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space (English) |
| Author:
|
Xu, Xian |
| Author:
|
Wang, Bingjin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
399-409 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions. (English) |
| Keyword:
|
sign-changing solution |
| Keyword:
|
operator equation in ordered Banach space |
| Keyword:
|
fixed point index |
| MSC:
|
47H07 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1212.47051 |
| idMR:
|
MR2597235 |
| DOI:
|
10.21136/MB.2009.140672 |
| . |
| Date available:
|
2010-07-20T18:12:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140672 |
| . |
| Reference:
|
[1] Amann, H.: On the number of solutions of nonlinear equations in ordered Banach spaces.J. Functional Anal. 11 (1972), 346-384. Zbl 0244.47046, MR 0358470, 10.1016/0022-1236(72)90074-2 |
| Reference:
|
[2] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces.SIAM Review 18 (1976), 620-709. Zbl 0345.47044, MR 0415432, 10.1137/1018114 |
| Reference:
|
[3] Bartsch, T., Chang, K. C., Wang, Z. Q.: On the Morse indices of sign changing solutions of nonlinear elliptic problems.Math. Z. 233 (2000), 655-677. Zbl 0946.35023, MR 1759266, 10.1007/s002090050492 |
| Reference:
|
[4] Dancer, E. N., Du, Y.: Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero.Proc. Royal Soc. Edinburgh 124 A (1994), 1165-1176. Zbl 0819.35054, MR 1313195 |
| Reference:
|
[5] Dancer, E. N., Du, Y.: On sign-changing solutions of certain semilinear elliptic problems.Appl. Anal. 56 (1995), 193-206. Zbl 0835.35051, MR 1383886, 10.1080/00036819508840321 |
| Reference:
|
[6] Deimling, K.: Nonlinear Functional Analysis.Springer (1985). Zbl 0559.47040, MR 0787404 |
| Reference:
|
[7] Pavel Drábek, Jaroslav Milota: Methods of Nonlinear Analysis.Applications to Differential Equations, Birkhäuser, Basel (2007). MR 2323436 |
| Reference:
|
[8] Fuyi Li: Solutions of nonlinear operator equations and applications.Ph. D. Thesis, Shandong University (1996). |
| Reference:
|
[9] Zhaoli Liu: Localized Critical Points in Banach Spaces and Sign Changing Solutions of Nonlinear $p$-Laplacian Equations.Topological Methods, Variational Methods. World Scientific Press, New Jersey (2002). MR 2011692 |
| Reference:
|
[10] Xian Xu: Multiple sign-changing solutions for some $m$-point boundary value problems.Electron. J. Differ. Equ. (2004), 89 1-14. Zbl 1058.34013, MR 2075428 |
| Reference:
|
[11] Xian Xu, Donal O'Regan: Multiplicity of sign-changing solutions for some four-point boundary value problem.Nonlinear Analysis 69 (2008), 434-447. MR 2426260, 10.1016/j.na.2007.05.030 |
| Reference:
|
[12] Xian Xu, Jingxian Sun: On sign-changing solution for some three-point boundary value problems.Nonlinear Analysis 59 (2004), 491-505. MR 2094426, 10.1016/j.na.2004.07.023 |
| Reference:
|
[13] Xian Xu, Jingxian Sun, Donal O'Regan: Nodal solutions for $m$-point boundary value problems using bifurcation methods.Nonlinear Analysis, 68 (2008), 3034-3046. MR 2404815, 10.1016/j.na.2007.02.043 |
| Reference:
|
[14] Kemei Zhang, Jingxian Sun: Multiple solutions for superlinear operator equations in Banach spaces and applications.Acta Math. Sinica (Chin. Ser.) 48 (2005), 99-108. MR 2128657 |
| . |
