Geodesic
Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions
Archivum mathematicum, Tome 44 (2008) no. 1, pp. 1-7 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 34B10, 34B15, 34B18, 34B27, 47N20
Keywords: multiple solutions; Leggett-Williams fixed point theorem; nonlinear boundary value problem; integral boundary conditions 
@article{ARM_2008_44_1_a0,
     author = {Belarbi, Abdelkader and Benchohra, Mouffak and Ouahab, Abdelghani},
     title = {Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions},
     journal = {Archivum mathematicum},
     pages = {1--7},
     year = {2008},
     volume = {44},
     number = {1},
     mrnumber = {2431225},
     zbl = {1212.34051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a0/}
}
TY  - JOUR
AU  - Belarbi, Abdelkader
AU  - Benchohra, Mouffak
AU  - Ouahab, Abdelghani
TI  - Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions
JO  - Archivum mathematicum
PY  - 2008
SP  - 1
EP  - 7
VL  - 44
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a0/
LA  - en
ID  - ARM_2008_44_1_a0
ER  - 
%0 Journal Article
%A Belarbi, Abdelkader
%A Benchohra, Mouffak
%A Ouahab, Abdelghani
%T Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions
%J Archivum mathematicum
%D 2008
%P 1-7
%V 44
%N 1
%U http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a0/
%G en
%F ARM_2008_44_1_a0
Belarbi, Abdelkader; Benchohra, Mouffak; Ouahab, Abdelghani. Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions. Archivum mathematicum, Tome 44 (2008) no. 1, pp. 1-7. http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a0/

[1] Agarwal, R. P., O’Regan, D.: Existence of three solutions to integral and discrete equations via the Leggett-Williams fixed point theorem. Rocky Mountain J. Math. 31 (2001), 23–35. | DOI | MR | Zbl

[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

[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. | MR | Zbl

[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. | DOI | MR

[5] Brykalov, S. A.: A second order nonlinear problem with two-point and integral boundary conditions. Georgian Math. J. 1 (1994), 243–249. | DOI | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[8] Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, San Diego, 1988. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[11] Krall, A. M.: The adjoint of a differential operator with integral boundary condition. Proc. Amer. Math. Soc. 16 (1965), 738–742. | DOI | MR

[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. | DOI | MR | Zbl

[13] Lomtatidze, A., Malaguti, L.: On a nonlocal boundary value problem for second order nonlinear singular differential equations. Georgian Math. J. 7 (2000), 133–154. | MR | Zbl