| Title:
|
Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions (English) |
| Author:
|
Belarbi, Abdelkader |
| Author:
|
Benchohra, Mouffak |
| Author:
|
Ouahab, Abdelghani |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
1-7 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the existence of multiple positive solutions for nonlinear boundary value problems with integral boundary conditions. We shall rely on the Leggett-Williams fixed point theorem. (English) |
| Keyword:
|
multiple solutions |
| Keyword:
|
Leggett-Williams fixed point theorem |
| Keyword:
|
nonlinear boundary value problem |
| Keyword:
|
integral boundary conditions |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
34B18 |
| MSC:
|
34B27 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1212.34051 |
| idMR:
|
MR2431225 |
| . |
| Date available:
|
2008-06-06T22:52:23Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108090 |
| . |
| Reference:
|
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| Reference:
|
[2] Agarwal, R. P., O’Regan, D., Wong, P. J. Y.: Positive Solutions of Differential, Difference and Integral Equations.Kluwer Academic Publishers, Dordrecht, 1999. MR 1680024 |
| Reference:
|
[3] Ahmad, B, Khan, R. A., Sivasundaram, S.: Generalized quasilinearization method for a first order differential equation with integral boundary condition.Dynam. Contin. Discrete Impuls. Systems, Ser. A Math. Anal. 12 (2005), 289–296. Zbl 1084.34007, MR 2170414 |
| Reference:
|
[4] Anderson, D., Avery, R., Peterson, A.: Three positive solutions to a discrete focal boundary value problem. Positive solutions of nonlinear problems.J. Comput. Appl. Math. 88 (1998), 103–118. MR 1609058, 10.1016/S0377-0427(97)00201-X |
| Reference:
|
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| Reference:
|
[6] Denche, M., Marhoune, A. L.: High-order mixed-type differential equations with weighted integral boundary conditions.Electron. J. Differential Equations 60 (2000), 1–10. Zbl 0967.35101, MR 1787207 |
| Reference:
|
[7] Gallardo, J. M.: Second-order differential operators with integral boundary conditions and generation of analytic semigroups.Rocky Mountain J. Math. 30 (2000), 265–1291. Zbl 0984.34014, MR 1810167 |
| Reference:
|
[8] Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones.Academic Press, San Diego, 1988. Zbl 0661.47045, MR 0959889 |
| Reference:
|
[9] Karakostas, G. L., Tsamatos, P. Ch.: Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems.Electron. J. Differential Equations 30 (2002), 17. Zbl 0998.45004, MR 1907706 |
| Reference:
|
[10] Khan, R. A.: The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions.Electron. J. Qual. Theory Differ. Equ. 19 (2003), 15. Zbl 1055.34033, MR 2039793 |
| Reference:
|
[11] Krall, A. M.: The adjoint of a differential operator with integral boundary condition.Proc. Amer. Math. Soc. 16 (1965), 738–742. MR 0181794, 10.1090/S0002-9939-1965-0181794-9 |
| Reference:
|
[12] Leggett, R. W., Williams, L.R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces.Indiana Univ. Math. J. 28 (1979), 673–688. Zbl 0421.47033, MR 0542951, 10.1512/iumj.1979.28.28046 |
| Reference:
|
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| . |
