Previous |  Up |  Next

Article

Title: Positive solutions for third order multi-point singular boundary value problems (English)
Author: Graef, John R.
Author: Kong, Lingju
Author: Yang, Bo
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 60
Issue: 1
Year: 2010
Pages: 173-182
Summary lang: English
.
Category: math
.
Summary: 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. (English)
Keyword: positive solution
Keyword: singular boundary value problem
Keyword: multi-point boundary condition
Keyword: nonlinear alternative of Leray-Schauder
MSC: 34B10
MSC: 34B15
MSC: 34B16
MSC: 34B18
MSC: 47N20
idZBL: Zbl 1224.34060
idMR: MR2595081
.
Date available: 2010-07-20T16:25:31Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/140560
.
Reference: [1] Agarwal, R. P., O'Regan, D.: Singular Differential and Integral Equations with Applications.Kluwer Academic Publishers, Boston (2003). Zbl 1055.34001, MR 2011127
Reference: [2] Agarwal, R. P., O'Regan, D.: Positive solutions for $(p, n-p)$ conjugate boundary value problems.J. Differential Equations 150 (1998), 462-473. Zbl 0920.34027, MR 1658664, 10.1006/jdeq.1998.3501
Reference: [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. Zbl 0863.34022, MR 1410892, 10.1006/jdeq.1996.0147
Reference: [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. Zbl 1127.34023, MR 2341553, 10.1016/j.jde.2007.05.007
Reference: [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. MR 0997609, 10.1016/0022-0396(89)90113-7
Reference: [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. Zbl 1168.34317, MR 2517736
Reference: [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. Zbl 1180.34020, MR 2518860
Reference: [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. Zbl 1153.34014, MR 2375585
Reference: [9] Eloe, P. W., Henderson, J.: Singular nonlinear $(k, n-k)$ conjugate boundary value problems.J. Differential Equations 133 (1997), 136-151. Zbl 0870.34031, MR 1426760, 10.1006/jdeq.1996.3207
Reference: [10] Eloe, P. W., Henderson, J.: Singular nonlinear boundary value problems for higher order ordinary differential equations.Nonlinear Anal. 17 (1991), 1-10. Zbl 0731.34015, MR 1113445, 10.1016/0362-546X(91)90116-I
Reference: [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 2295682
Reference: [12] Maroun, M.: Positive solutions to an third-order right focal boundary value problem.Comm. Appl. Nonlinear Anal. 12 (2005), 71-82. MR 2142919
Reference: [13] Kong, L., Kong, Q.: Positive solutions of higher-order boundary value problems.Proc. Edinburgh Math. Soc. 48 (2005), 445-464. Zbl 1084.34023, MR 2157255
Reference: [14] Rachůnková, I., Staněk, S.: Sturm-Liouville and focal higher order BVPs with singularities in phase variables.Georgian Math. J. 10 (2003), 165-191. MR 1990696, 10.1515/GMJ.2003.165
Reference: [15] O'Regan, D.: Existence of solutions to third order boundary value problems.Proc. Royal Irish Acad. Sect. A 90 (1990), 173-189. Zbl 0695.34015, MR 1150456
.

Files

Files Size Format View
CzechMathJ_60-2010-1_15.pdf 249.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo