×

Positive solutions to second order four-point boundary value problems for impulsive differential equations. (English) Zbl 1255.34025

Summary: In this paper, by using the Leggett-Williams theorem we present sufficient conditions which guarantee the existence of three positive solutions to second order four-point boundary value problems for impulsive differential equations.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B37 Boundary value problems with impulses for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Agarwal, R. P.; Franco, D.; O’Regan, D., Singular boundary value problems for first and second order impulsive differential equations, Aequat. Math., 69, 83-96 (2005) · Zbl 1073.34025
[2] Agarwal, R. P.; O’Regan, D., A multiplicity result for second order impulsive differential equations via the Leggett Williams fixed point theorem, Appl. Math. Comput., 161, 433-439 (2005) · Zbl 1070.34042
[3] Agarwal, R. P.; O’Regan, D.; Wong, P. J.Y., Positive Solutions of Differential, Difference and Integral Equations (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0923.39002
[4] Bai, Z.; Ge, W.; Wang, Y., Multiplicity results for some second-order four-point boundary-value problems, Nonlinear Anal., 60, 491-500 (2005) · Zbl 1088.34015
[5] Bai, Z.; Du, Z., Positive solutions for some second-order four-point boundary value problems, J. Math. Anal. Appl., 330, 34-50 (2007) · Zbl 1115.34016
[6] Guo, D.; Liu, X., Multiple positive solutions of boundary-value problems for impulsive differential equations, Nonlinear Anal., 25, 327-337 (1995) · Zbl 0840.34015
[7] Jankowski, T., Positive solutions of three-point boundary value problems for second order impulsive differential equations with advanced arguments, Appl. Math. Comput., 197, 179-189 (2008) · Zbl 1145.34355
[8] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Ordinary Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[9] Lee, E. K.; Lee, Y.-H., Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations, Appl. Math. Comput., 158, 745-759 (2004) · Zbl 1069.34035
[10] Leggett, R. W.; Williams, L. R., Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana Univ. Math. J., 28, 673-688 (1979) · Zbl 0421.47033
[11] Lin, X.; Jiang, D., Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations, J. Math. Anal. Appl., 321, 501-514 (2006) · Zbl 1103.34015
[12] Liu, B., Positive solutions of a nonlinear four-point boundary value problems, Appl. Math. Comput., 155, 179-203 (2004) · Zbl 1068.34011
[13] Liu, B., Positive solutions of a nonlinear four-point boundary value problems in Banach spaces, J. Math. Anal. Appl., 305, 253-276 (2005) · Zbl 1073.34075
[14] Samoilenko, A. M.; Perestyuk, N. A., Impulsive Differential Equations (1995), World Scientific: World Scientific Singapore · Zbl 0837.34003
[15] Yan, J., Existence of positive solutions of impulsive functional differential equations with two parameters, J. Math. Anal. Appl., 327, 854-868 (2007) · Zbl 1114.34052
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.