Ahmad, Bashir; Alsaedi, Ahmed Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type. (English) Zbl 1179.45008 Nonlinear Anal., Hybrid Syst. 3, No. 4, 501-509 (2009). The authors discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. Keeping in view the importance of functional integro-differential equations and anti-periodic boundary conditions, they apply the monotone iterative technique (MIT) to prove the existence of extremal solutions for a first order nonlinear impulsive functional integro-differential equation of mixed type with anti-periodic boundary conditions. The MIT coupled with the method of upper and lower solutions manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set, generated by the lower and upper solutions. Reviewer: Kun Soo Chang (Seoul) Cited in 14 Documents MSC: 45J05 Integro-ordinary differential equations 45L05 Theoretical approximation of solutions to integral equations 45G10 Other nonlinear integral equations Keywords:impulsive functional integro-differential equations; upper and lower solutions; monotone iterative technique; minimal and maximal solutions; anti-periodic boundary conditions PDFBibTeX XMLCite \textit{B. Ahmad} and \textit{A. Alsaedi}, Nonlinear Anal., Hybrid Syst. 3, No. 4, 501--509 (2009; Zbl 1179.45008) Full Text: DOI References: [1] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002 [2] Zavalishchin, S. 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