×

Multiple positive solutions for \(n\)th-order impulsive integro-differential equations in Banach spaces. (English) Zbl 1069.45010

The author considers a boundary value problem of an \(n\)th-order impulsive integro-differential equation on an infinite interval and, using the fixed point index theory for completely continuous operators, proves the existence of multiple positive solutions.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45M20 Positive solutions of integral equations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
45G10 Other nonlinear integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Banas, J.; Goebel, K., Measures of Noncompactness in Banach Spaces (1980), Marcel Dekker: Marcel Dekker New York/Basel · Zbl 0441.47056
[2] Erbe, L. H.; Liu, X. Z., Quasisolutions of nonlinear impulsive equations in abstract cones, Appl. Anal., 34, 231-250 (1989) · Zbl 0662.34015
[3] Guo, D., Periodic boundary value problems for second order impulsive integro-differential equations in Banach spaces, Nonlinear Anal., 28, 983-997 (1997) · Zbl 0957.34057
[4] Guo, D., Second order impulsive integro-differential equations on unbounded domains in Banach spaces, Nonlinear Anal., 35, 413-423 (1999) · Zbl 0917.45010
[5] Guo, D., Existence of solutions for \(n\) th order impulsive integro-differential equations in a Banach space, Nonlinear Anal., 47, 741-752 (2001) · Zbl 1042.34584
[6] 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
[7] Guo, D., Multiple positive solutions for first order nonlinear impulsive integro-differential equations in a Banach space, Appl. Math. Comput., 143, 233-249 (2003) · Zbl 1030.45009
[8] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press Boston · Zbl 0661.47045
[9] Guo, D.; Lakshmikantham, V.; Liu, X. Z., Nonlinear Integral Equations in Abstract Spaces (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0866.45004
[10] Guo, D.; Liu, X. Z., Extremal solutions of nonlinear impulsive integro-differential equations in Banach spaces, J. Math. Anal. Appl., 177, 538-552 (1993) · Zbl 0787.45008
[11] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[12] Liu, X. Z., Nonlinear boundary value problems for first order impulsive integro-differential equations, Appl. Anal., 36, 119-130 (1990) · Zbl 0671.34018
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.