Existence of positive solutions for Sturm-Liouville boundary value problems on the half-line. (English) Zbl 1104.34020

The authors derive sufficient conditions to guarantee some properties of the positive solutions of the considered Sturm-Liouville problem. It is interesting that the nonlinear term can be sign-changing.


34B24 Sturm-Liouville theory
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
Full Text: DOI


[1] O’Regan, D., Theory of singular boundary value problems, (1994), World Scientific Singapore · Zbl 0808.34022
[2] Agarwal, R.P.; O’Regan, D., Infinite interval problems for differential, difference and integral equations, (2001), Kluwer Academic · Zbl 1003.39017
[3] Agarwal, R.P.; O’Regan, D., Fixed point theory for self maps between Fréchet spaces, J. math. anal. appl., 256, 498-512, (2001) · Zbl 0997.47044
[4] Yan, B., Boundary value problems on the half-line with impulse and infinite delay, J. math. anal. appl., 259, 94-114, (2001) · Zbl 1009.34059
[5] Jiang, D.; Agarwal, R.P., A uniqueness and existence theorem for s singular third-order boundary value problem on \([0, \infty)\), Appl. math. lett., 15, 445-451, (2002) · Zbl 1021.34020
[6] Frigon, M., Fixed point results for compact maps on closed subsets of Fréchet spaces and applications to differential and integral equations, Bull. belg. math. soc., 9, 23-37, (2002) · Zbl 1026.47047
[7] Frigon, M.; O’Regan, D., Fixed point of cone-compressing and cone-extending operators in Fréchet spaces, Bull. London math. soc., 35, 672-680, (2003) · Zbl 1041.47040
[8] Ma, R., Existence of positive solution for second-order boundary value problems on infinite intervals, Appl. math. lett., 16, 33-39, (2003) · Zbl 1046.34045
[9] Bai, C.; Fang, J., On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals, J. math. anal. appl., 282, 711-731, (2003) · Zbl 1036.34075
[10] Ge, W.; Ren, J., New existence theorem of positive solutions for sturm – liouville boundary value problems, Appl. math. comput., 148, 631-644, (2004) · Zbl 1055.34053
[11] Yan, B.; Liu, Y., Unbounded solutions of the singular boundary value problems for second order differential equations on the half-line, Appl. math. comput., 147, 629-644, (2004) · Zbl 1045.34009
[12] Zhong, C.; Fan, X.; Chen, W., The introduction of nonlinear functional analysis, (1998), Lanzhou University Press PR China
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.