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Extremal Solutions of Periodic Boundary Value Problems for First-Order Impulsive Integrodifferential Equations of Mixed-Type on Time Scales
Boundary Value Problems volume 2007, Article number: 073176 (2007)
Abstract
We consider the existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive integrodifferential equations of mixed-type on time scales by establishing a comparison result and using the monotone iterative technique.
References
Bohner M, Peterson A: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358.
Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348.
Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.
Henderson J: Double solutions of impulsive dynamic boundary value problems on a time scale. Journal of Difference Equations and Applications 2002,8(4):345–356. 10.1080/1026190290017405
Benchohra M, Henderson J, Ntouyas SK, Ouahab A: On first order impulsive dynamic equations on time scales. Journal of Difference Equations and Applications 2004,10(6):541–548. 10.1080/10236190410001667986
Atici FM, Biles DC: First- and second-order dynamic equations with impulse. Advances in Difference Equations 2005,2005(2):119–132. 10.1155/ADE.2005.119
Liu X, Guo D: Periodic boundary value problems for impulsive integro-differential equations of mixed type in Banach spaces. Chinese Annals of Mathematics. Series B 1998,19(4):517–528.
Ladde GS, Sathananthan S: Periodic boundary value problem for impulsive integro-differential equations of Volterra type. Journal of Mathematical and Physical Sciences 1991,25(2):119–129.
Erbe LH, Guo DJ: Periodic boundary value problems for second order integrodifferential equations of mixed type. Applicable Analysis 1992,46(3–4):249–258. 10.1080/00036819208840124
Lakshmikantham V, BaÄnov DD, Simeonov PS: Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics. Volume 6. World Scientific, Teaneck, NJ, USA; 1989:xii+273.
Kelley WG, Peterson AC: Difference Equations. An Introduction with Applications. Academic Press, Boston, Mass, USA; 1991:xii+455.
Xing Y, Han M, Zheng G: Initial value problem for first-order integro-differential equation of Volterra type on time scales. Nonlinear Analysis: Theory, Methods & Applications 2005,60(3):429–442.
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Li, Y., Zhang, H. Extremal Solutions of Periodic Boundary Value Problems for First-Order Impulsive Integrodifferential Equations of Mixed-Type on Time Scales. Bound Value Probl 2007, 073176 (2007). https://doi.org/10.1155/2007/73176
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DOI: https://doi.org/10.1155/2007/73176