| Title:
|
Existence and iteration of positive solutions for a singular two-point boundary value problem with a $p$-Laplacian operator (English) |
| Author:
|
Ma, De-xiang |
| Author:
|
Ge, Wei-Gao |
| Author:
|
Gui, Zhan-Ji |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
135-152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation $(\phi _p(u^{\prime }))^{\prime }+q(t)f(u)=0$, $0<t<1$, where $\phi _p(s):=|s|^{p-2}s$, $p>1$, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q(t)$ may be singular at $t=0,1$. (English) |
| Keyword:
|
iteration |
| Keyword:
|
symmetric and monotone positive solution |
| Keyword:
|
nonlinear boundary value problem |
| Keyword:
|
$p$-Laplacian |
| MSC:
|
34A45 |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
34B18 |
| idZBL:
|
Zbl 1174.34018 |
| idMR:
|
MR2309955 |
| . |
| Date available:
|
2009-09-24T11:44:34Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128161 |
| . |
| Reference:
|
[1] J. Wang: The existence of positive solutions for the one-dimensional $p$-Laplacian.Proc. Am. Math. Soc. 125 (1997), 2275–2283. Zbl 0884.34032, MR 1423340, 10.1090/S0002-9939-97-04148-8 |
| Reference:
|
[2] L. Kong, J. Wang: Multiple positive solutions for the one-dimensional $p$-Laplacian.Nonlinear Analysis 42 (2000), 1327–1333. MR 1784078, 10.1016/S0362-546X(99)00143-1 |
| Reference:
|
[3] D. Guo, V. Lakshmikantham: Nonlinear Problems in Abstract. Cones.Academic Press, Boston, 1988. MR 0959889 |
| Reference:
|
[4] X. He, W. Ge: Twin positive solutions for the one-dimensional $p$-Laplacian.Nonlinear Analysis 56 (2004), 975–984. Zbl 1061.34013, MR 2038732, 10.1016/j.na.2003.07.022 |
| Reference:
|
[5] R. I. Avery, C. J. Chyan, and J. Henderson: Twin solutions of boundary value problems for ordinary differential equations and finite difference equations.Comput. Math. Appl. 42 (2001), 695–704. MR 1838025, 10.1016/S0898-1221(01)00188-2 |
| Reference:
|
[6] R. P. Agarwal, H. Lü and D. O’Regan: Eigenvalues and the one-dimensional $p$-Laplacian.J. Math. Anal. Appl. 266 (2002), 383–340. MR 1880513, 10.1006/jmaa.2001.7742 |
| Reference:
|
[7] Y. Guo, W. Ge: Three positive solutions for the one-dimensional $p$-Laplacian.Nonlinear Analysis 286 (2003), 491–508. Zbl 1045.34005, MR 2008845 |
| Reference:
|
[8] H. Amann: Fixed point equations and nonlinear eigenvalue problems in order Banach spaces.SIAM Rev. 18 (1976), 620–709. MR 0415432, 10.1137/1018114 |
| . |
