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Second order impulsive integro-differential equations on unbounded domains in Banach spaces. (English) Zbl 0917.45010

The author investigates the minimal nonnegative solution for a second-order nonlinear impulsive integro-differential equation of Volterra type on an infinite interval with an infinite number of impulsive times in a Banach space.

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
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References:

[2] Guo, D.; Liu, X. Z., Multiple positive solutions of boundary value problems for impulsive differential equations, Nonlinear Analysis, 25, 327-337 (1995) · Zbl 0840.34015
[3] Guo, D., Existence of solutions of boundary value problems for nonlinear second order impulsive differential equations in Banach spaces, J. Math. Anal. Appl., 181, 407-421 (1994) · Zbl 0807.34076
[4] 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
[5] Guo, D.; Liu, X. Z., Impulsive integro-differential equations on unbounded domain in a Banach space, Nonlinear Studies, 3, 49-57 (1996) · Zbl 0864.45009
[7] Du, Y., Fixed points of increasing operators in ordered Banach spaces and applications, Appl. Anal., 38, 1-20 (1990) · Zbl 0671.47054
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