Positive solutions for third order semipositone boundary value problems. (English) Zbl 1173.34313

Graef, John R.; Kong, Lingju

Appl. Math. Lett. 22, No. 8, 1154-1160 (2009).

Summary: We obtain some sufficient conditions for the existence of positive solutions of a third order semipositone boundary value problem with a multi-point boundary condition. Applications of our results to some special problems are also discussed.

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

positive solutions; semipositone boundary value problems; multi-point boundary condition

References:

[1]	Anderson, D.R.; Davis, J.M., Multiple solutions and eigenvalues for third-order right focal boundary value problems, J. math. anal. appl., 267, 135-157, (2002) · Zbl 1003.34021
[2]	Clark, S.L.; Henderson, J., Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations, Proc. amer. math. soc., 134, 3363-3372, (2006) · Zbl 1120.34010
[3]	Du., Z.; Liu, W.; Lin, X., Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations, J. math. anal. appl., 335, 1207-1218, (2007) · Zbl 1133.34011
[4]	Eloe, P.W.; Ahmad, B., Positive solutions of a nonlinear \(n\)th order boundary value problem with nonlocal conditions, Appl. math. lett., 18, 521-527, (2005) · Zbl 1074.34022
[5]	Graef, J.R.; Kong, L.; Yang, B., Existence of solutions for a higher order multi-point boundary value problem, Result. math., 53, 77-101, (2009) · Zbl 1173.34008
[6]	Graef, J.R.; Yang, B., Positive solutions of a third order nonlinear boundary value problem, Discrete contin. dynam. syst. S, 1, 89-97, (2008) · Zbl 1153.34014
[7]	Henderson, J.; Ntouyas, S.K., Positive solutions for systems of \(n\)th order three-point nonlocal boundary value problems, Electron J. qual. theory diff. equ., 18, 12, (2007), (electronic) · Zbl 1182.34029
[8]	Aris, R., Introduction to the analysis of chemical reactors, (1965), Prentice Hall New Jersey
[9]	Agarwal, R.P.; Grace, S.R.; O’regan, D., Semipositone higher-order differential equations, Appl. math. lett., 17, 201-207, (2004) · Zbl 1072.34020
[10]	Anuradha, V.; Hai, D.D.; Shivaji, R., Existence results for superlinear semipositone BVP’s, Proc. amer. math. soc., 124, 757-763, (1996) · Zbl 0857.34032
[11]	Lan, K.Q., Positive solutions of semi-positone Hammerstein integral equations and applications, Comm. pure appl. anal., 6, 441-451, (2007) · Zbl 1134.45005
[12]	Lan, K.Q., Multiple positive solutions of semi-positone sturm – liouville boundary value problems, Bull. London math. soc., 38, 283-293, (2006) · Zbl 1094.34014
[13]	Ma, R., Positive solutions for semipositone \((k, n - k)\) conjugate boundary value problem, J. math. anal. anal., 252, 220-229, (2000) · Zbl 0979.34012
[14]	Ma, R., Existence of positive solutions for superlinear semipositone \(m\)-point boundary value problems, Proc. Edinburgh math. soc., 46, 279-292, (2003) · Zbl 1069.34036
[15]	Zhang, X.; Liu, L.; Wu, Y., Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems, Nonlinear anal., 68, 97-108, (2008) · Zbl 1135.34016
[16]	Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press Orlanda · Zbl 0661.47045