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Nonlinear boundary value problem of first order impulsive functional differential equations. (English) Zbl 1102.34052
The authors are concerned with boundary value problems for first-order impulsive functional-differential equations. By using lower and upper solutions and monotone iterative techniques, they establish several existence results. Examples to illustate the efficiency of the results obtained are discussed.

MSC:
34K10Boundary value problems for functional-differential equations
34K45Functional-differential equations with impulses
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References:
[1] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[2] Nieto, J. J.; Rodríguez-López, R.: Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions. Comput. math. Appl. 40, 433-442 (2000) · Zbl 0958.34055
[3] Xu, H. -K.; Liz, E.: Boundary value problems for functional differential equations. Nonlinear anal. 41, 971-988 (2000) · Zbl 0972.34054
[4] Nieto, J. J.: Differential inequalities of functional perturbations of first-order ordinary differential equations. Appl. math. Lett. 15, 173-179 (2002) · Zbl 1014.34060
[5] Nieto, J. J.; Rodríguez-López, R.: Remarks on periodic boundary value problems for functional differential equations. J. comput. Appl. math. 158, 339-353 (2003) · Zbl 1036.65058
[6] Jiang, D. Q.; Nieto, J. J.; Zuo, W. J.: On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations. J. math. Anal. appl. 289, 691-699 (2004) · Zbl 1134.34322
[7] Jankowski, T.: Existence of solutions of boundary value problems for differential equations with delayed argument. J. comput. Appl. math. 156, 239-252 (2003) · Zbl 1048.34107
[8] Jankowski, T.: Advanced differential equations with nonlinear boundary conditions. J. math. Anal. appl. 304, 490-503 (2005) · Zbl 1092.34032
[9] Yebdri, M.; Bouguima, S. M.; Arino, O.: An iterative method for functional differential equations. Appl. math. Comput. 161, 265-269 (2005) · Zbl 1071.34064
[10] Sun, J. T.: Stability criteria of impulsive differential system. Appl. math. Comput. 156, 85-91 (2004) · Zbl 1062.34006
[11] Sun, J. T.; Zhang, Y. P.; Wu, Q. D.: Less conservative conditions for asymptotic stability of impulsive control systems. IEEE trans. Automat. control 48, 829-831 (2003)
[12] Ding, W.; Mi, J. R.; Han, M. A.: Periodic boundary value problem for the first order impulsive functional differential equations. Appl. math. Comput. 165, 433-446 (2005) · Zbl 1081.34081
[13] Ding, W.; Han, M. A.: Periodic boundary value problem for the second order impulsive functional differential equations. Appl. math. Comput. 155, 709-726 (2004) · Zbl 1064.34067
[14] Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations. (1995) · Zbl 0837.34003
[15] Rogovchenko, Y. V.: Impulsive evolution systems: Main results and new trends. Dyn. contin. Discrete impuls syst. 3, 57-88 (1997) · Zbl 0879.34014
[16] Nieto, J. J.: Basic theory or nonresonance impulsive periodic problems of first order. J. math. Anal. appl. 205, 423-433 (1997) · Zbl 0870.34009
[17] Rachunkova, I.; Tvrdy, M.: Existence results for impulsive second-order periodic problems. Nonlinear anal. 59, 133-146 (2004)
[18] Franco, D.: A contribution to the study of functional differential equations with impulses. Math. nachr. 218, 49-60 (2000) · Zbl 0966.34073
[19] Tang, S.; Chen, L.: Density-dependent birth rate, birth pulses and their population dynamic consequences. J. math. Biol. 44, 185-199 (2002) · Zbl 0990.92033
[20] Yan, J.: Differential inequalities of functional, existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka -- Volterra systems. Math. comput. Modelling 40, 509-518 (2004) · Zbl 1112.34052
[21] Nieto, J. J.: Impulsive resonance periodic problems of first order. Appl. math. Lett. 15, 489-493 (2002) · Zbl 1022.34025
[22] Nieto, J. J.: Periodic boundary value problems for first-order impulsive ordinary differential equations. Nonlinear anal. 51, 1223-1232 (2002) · Zbl 1015.34010
[23] Franco, D.; Nieto, J. J.; Oregan, D.: Anti-periodic boundary value problem for nonlinear first order ordinary differential equations. Math. inequal. Appl. 6, 477-485 (2003) · Zbl 1097.34015
[24] Franco, D.; Nieto, J. J.; Oregan, D.: Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions. Appl. math. Comput. 153, 793-802 (2004) · Zbl 1058.34015
[25] Luo, Z. G.; Shen, J. H.; Nieto, J. J.: Anti-periodic boundary value problems for first order impulsive ordinary differential equations. Comput. math. Appl. 49, 253-261 (2005) · Zbl 1084.34018
[26] Cabada, A.; Ferreiro, J. B.; Nieto, J. J.: Greens function and comparison principles for first order periodic differential equations with piecewise constant arguments. J. math. Anal. appl. 291, 690-697 (2004) · Zbl 1057.34089
[27] Nieto, J. J.; Rodríguez-López, R.: Greens function for second-order periodic boundary value problems with piecewise constant arguments. J. comput. Appl. math. 304, 33-57 (2005) · Zbl 1078.34046
[28] J.J. Nieto, R. Rodríguez-López, Periodic boundary value problems for non-Lipschitzian impulsive functional differential equations, J. Comput. Appl. Math., in press