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Existence results and monotone iterative technique for impulsive hybrid functional differential systems with anticipation and retardation. (English) Zbl 1142.34049

The authors discuss existence results for impulsive hybrid functional differential equations with anticipation and retardation. They use the monotone iterative technique coupled with upper and lower solutions.

MSC:

34K45 Functional-differential equations with impulses
34K07 Theoretical approximation of solutions to functional-differential equations
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References:

[1] D.M. Dubois, Theory of computing anticipatory systems based on differential delayed-advanced difference equations. in: Computing anticipatory systems (Liège, 2001), 3-16, AIP Conf. Proc., 627, Amer. Inst. Phys., Melville, NY, 2002.; D.M. Dubois, Theory of computing anticipatory systems based on differential delayed-advanced difference equations. in: Computing anticipatory systems (Liège, 2001), 3-16, AIP Conf. Proc., 627, Amer. Inst. Phys., Melville, NY, 2002.
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[6] Lakshmikantham, V.; Zhang, B. G., Monotone iterative technique for impulsive differential equations, Appl. Anal., 22, 227-233 (1986) · Zbl 0576.34061
[7] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[8] Yan, B.; Fu, X., Monotone iterative technique for impulsive delay differential equations, Proc. Indian Acad. Sci. (Math. Sci.), 111, 351-363 (2001) · Zbl 0993.34071
[9] Bhaskar, T. G.; Lakshmikantham, V.; Devi, J. V., Monotone iterative technique for functional differential equations with retardation and anticipation, Nonlinear Anal., 66, 2237-2242 (2007) · Zbl 1121.34065
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