×

Positive solutions of an infinite boundary value problem for \(n\)th-order nonlinear impulsive singular integro-differential equations in Banach spaces. (English) Zbl 1159.45002

This paper deals with the existence of positive solutions for an infinite boundary value problem of \(n\)th-order nonlinear impulsive singular integro-differential equations on the half-line in a Banach space by means of fixed point theory. A concrete example is detailed.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[2] Guo, D., Existence of solutions for nth order impulsive integro-differential equations in a Banach space, Nonlinear Anal., 47, 741-752 (2001) · Zbl 1042.34584
[3] Guo, D., A class of \(n\) th-order impulsive integro-differential equations in Banach spaces, Comput. Math. Appl., 44, 1339-1356 (2002) · Zbl 1035.45009
[4] Guo, D., Multiple positive solutions of a boundary value problem for \(n\) th-order impulsive integro-differential equations in a Banach space, Nonlinear Anal., 56, 985-1006 (2004) · Zbl 1054.45007
[5] Guo, D., Multiple positive solutions for \(n\) th-order impulsive integro-differential equations in Banach spaces, Nonlinear Anal., 60, 955-976 (2005) · Zbl 1069.45010
[6] Guo, D.; Liu, X. Z., Extremal solutions for a boundary value problem of \(n\) th-order impulsive integro-differential equations in a Banach space, Dyn. Contin. Discrete Impuls. Syst., 13, 599-619 (2006) · Zbl 1113.45017
[7] Liu, L.; Liu, Z.; Wu, Y., Infinite BVPs for \(n\)-th order nonlinear impulsive integro-differential equations in Banach spaces, Nonlinear Anal., 67, 2670-2679 (2007) · Zbl 1124.45008
[8] Guo, D., Existence of positive solutions for \(n\) th-order nonlinear impulsive singular integro-differential equations in Banach spaces, Nonlinear Anal. (2007)
[9] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press Inc.: Academic Press Inc. Boston · Zbl 0661.47045
[10] Guo, D.; Lakshmikantham, V.; Liu, X. Z., Nonlinear Integral Equations in Abstract Spaces (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0866.45004
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.