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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:
45N05Abstract integral equations, integral equations in abstract spaces
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
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References:
[1] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. · Zbl 0719.34002
[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
[6] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988. · Zbl 0661.47045
[7] Du, Y.: Fixed points of increasing operators in ordered Banach spaces and applications. Appl. anal. 38, 1-20 (1990) · Zbl 0671.47054