Ahmad, Bashir; Sivasundaram, S. Existence results and monotone iterative technique for impulsive hybrid functional differential systems with anticipation and retardation. (English) Zbl 1142.34049 Appl. Math. Comput. 197, No. 2, 515-524 (2008). 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. Reviewer: Mustapha Yebdri (Tlemcen) Cited in 10 Documents MSC: 34K45 Functional-differential equations with impulses 34K07 Theoretical approximation of solutions to functional-differential equations Keywords:hybrid differential equations with anticipation and retardation; impulsive differential equations; upper and lower solution PDF BibTeX XML Cite \textit{B. Ahmad} and \textit{S. Sivasundaram}, Appl. Math. Comput. 197, No. 2, 515--524 (2008; Zbl 1142.34049) Full Text: DOI OpenURL 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. [2] Dubois, D.M., Extension of the kaldor – kalecki model of business cycle with a computational anticipated capital stock, Int. J. organ. transform. social change, 1, 63-80, (2003) [3] Dubois, D.M., Theory of incursive synchronization and application to the anticipation of a chaotic epidemic, Int. J. comput. anticipatory syst., 10, 3-18, (2001) [4] Bhaskar, T.G.; Lakshmikantham, V., Functional differential systems with retardation and anticipation, Nonlinear anal. real. world appl., 8, 865-871, (2007) · Zbl 1138.34029 [5] Ladde, G.S.; Lakshmikantham, V.; Vatsala, A.S., Monotone iterative technique for nonlinear differential equations, (1985), Pitman Advanced Publishing Program Boston · Zbl 0658.35003 [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 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 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.