Positive solutions for third order multi-point singular boundary value problems
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 173-182 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.
We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.
Classification : 34B10, 34B15, 34B16, 34B18, 47N20
Keywords: positive solution; singular boundary value problem; multi-point boundary condition; nonlinear alternative of Leray-Schauder
@article{CMJ_2010_60_1_a14,
     author = {Graef, John R. and Kong, Lingju and Yang, Bo},
     title = {Positive solutions for third order multi-point singular boundary value problems},
     journal = {Czechoslovak Mathematical Journal},
     pages = {173--182},
     year = {2010},
     volume = {60},
     number = {1},
     mrnumber = {2595081},
     zbl = {1224.34060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a14/}
}
TY  - JOUR
AU  - Graef, John R.
AU  - Kong, Lingju
AU  - Yang, Bo
TI  - Positive solutions for third order multi-point singular boundary value problems
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 173
EP  - 182
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a14/
LA  - en
ID  - CMJ_2010_60_1_a14
ER  - 
%0 Journal Article
%A Graef, John R.
%A Kong, Lingju
%A Yang, Bo
%T Positive solutions for third order multi-point singular boundary value problems
%J Czechoslovak Mathematical Journal
%D 2010
%P 173-182
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a14/
%G en
%F CMJ_2010_60_1_a14
Graef, John R.; Kong, Lingju; Yang, Bo. Positive solutions for third order multi-point singular boundary value problems. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 173-182. http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a14/

[1] Agarwal, R. P., O'Regan, D.: Singular Differential and Integral Equations with Applications. Kluwer Academic Publishers, Boston (2003). | MR | Zbl

[2] Agarwal, R. P., O'Regan, D.: Positive solutions for $(p, n-p)$ conjugate boundary value problems. J. Differential Equations 150 (1998), 462-473. | DOI | MR | Zbl

[3] Agarwal, R. P., O'Regan, D.: Singular boundary value problems for superlinear second order ordinary and delay differential equations. J. Differential Equations 130 (1996), 333-355. | DOI | MR | Zbl

[4] Chu, J., Torres, P. J., Zhang, M.: Periodic solutions of second order non-autonomous singular dynamical systems. J. Differential Equations 239 (2007), 196-211. | DOI | MR | Zbl

[5] Gatica, J. A., Oliver, V., Waltman, P.: Singular nonlinear boundary value problems for second order differential equations. J. Differential Equations 79 (1989), 62-78. | DOI | MR

[6] Graef, J. R., Henderson, J., Yang, B.: Positive solutions to a singular third order nonlocal boundary value problem. Indian J. Math. 50 (2008), 317-330. | MR | Zbl

[7] Graef, J. R., Henderson, J., Yang, B.: Existence of positive solutions of a higher order nonlocal singular boundary value problem. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16, Supplement S1 (2009), 147-152. | MR | Zbl

[8] Graef, J. R., Yang, B.: Positive solutions of a third order nonlocal boundary value problem. Discrete Contin. Dyn. Syst. Ser. S 1 (2008), 89-97. | MR | Zbl

[9] Eloe, P. W., Henderson, J.: Singular nonlinear $(k, n-k)$ conjugate boundary value problems. J. Differential Equations 133 (1997), 136-151. | DOI | MR | Zbl

[10] Eloe, P. W., Henderson, J.: Singular nonlinear boundary value problems for higher order ordinary differential equations. Nonlinear Anal. 17 (1991), 1-10. | DOI | MR | Zbl

[11] Maroun, M.: Positive solutions to an $N^{th}$ order right focal boundary value problem. Electron. J. Qual. Theory Diff. Equ. 2007 17 (electronic). | MR

[12] Maroun, M.: Positive solutions to an third-order right focal boundary value problem. Comm. Appl. Nonlinear Anal. 12 (2005), 71-82. | MR

[13] Kong, L., Kong, Q.: Positive solutions of higher-order boundary value problems. Proc. Edinburgh Math. Soc. 48 (2005), 445-464. | MR | Zbl

[14] Rachůnková, I., Staněk, S.: Sturm-Liouville and focal higher order BVPs with singularities in phase variables. Georgian Math. J. 10 (2003), 165-191. | DOI | MR

[15] O'Regan, D.: Existence of solutions to third order boundary value problems. Proc. Royal Irish Acad. Sect. A 90 (1990), 173-189. | MR | Zbl