Abstract
In this paper, we established the general comparison prinples for IVP of impulsive differential equations with time variables, which strictly extend and improve the previous comparison results obtained by V.Lakes.et.al. and S.K.Kaul([3]–[7]). With the general comparison results, we constructed the monotone iterative sequences of solutions for IVP of such equations which converges the maximal and minimal solutions, repectively.
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G.S. Laddle, V. Lakshmikantham and A.S. Vatala,Monotone iterative technique for Nonlinear diferential equations, Pitman Advance Publishing Program, Bostone (1985.).
V. Lakshmikantham, D.D. Bainov and P.S. Simeonov,Theory of impulsive differential equations, World Scientific, Singapore (1989).
V. Laks., N.S. Papageorgiou, J. Vasundhara Devi,The method of upper and lower solutions and monotone technique for impulsive diferential equations with variable moments, Applicable Analysis51 (1993), 41–54.
S.K. Kaul,Monotone iterative technique for impulsive diferential equations with variable times, Nonlinear World2 (1995), 341–345.
S.K. Kaul,The periodic boundary value problem for impulsive diferential equations with variable times, Nonlinear Times and Digest2 (1995), 107–116.
S.K. Kaul, V. Lakshmikantham and S. Leela,Extremal solutions, comparison principle and stability criteria for impulsive diferential equations with variable times, Nonl. Anal. Appli., V.22, N.10 (1994), 1263–1270.
V. Lakshmikantham, S. Leela and S. Kaul,Comparison principle for impulsive diferential equations with variable times and stability theory, Nonl. Anal., V.22, N.4 (1994), 499–503.
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Qi, J., Liu, Y. Monotone iterative technique for impulsive differential equations with time variables. Korean J. Comput. & Appl. Math. 7, 419–432 (2000). https://doi.org/10.1007/BF03012203
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DOI: https://doi.org/10.1007/BF03012203