Previous |  Up |  Next

Article

Keywords:
impulsive differential equations; periodic boundary value problem; monotone iterative technique
Summary:
In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.
References:
[1] Cabada A., Nieto J.J.: A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems. J. Math. Anal. Appl. 151 (1990), 181-189. MR 1069454 | Zbl 0719.34039
[2] Hale J.: Theory of functional differential equations. Springer-Verlag, New York, 1977. MR 0508721 | Zbl 1092.34500
[3] Lakshmikantham V., Bainov D.D., Simeonov P.S.: Theory of impulsive differential equations. World Scientific, Singapore, 1989. MR 1082551 | Zbl 0719.34002
[4] Hu S., Lakshmikantham V.: Periodic boundary value problems for second order impulsive differential systems. Nonlinear Anal. 13 (1989), 75-85. MR 0973370 | Zbl 0712.34033
[5] Ladde G.S., Lakshmikantham V., Vatsala A.S.: Monotone iterative techniques for nonlinear differential equations. Pitman Advanced Publishing Program, 1985. MR 0855240 | Zbl 0658.35003
[6] Liu X.: Nonlinear boundary value problems for first order impulsive integro-differential equations. Applicable Anal. 36 (1989), 119-130. MR 1040882 | Zbl 0688.45015
[7] Liz E., Nieto J.J.: Periodic solutions of discontinuous impulsive differential systems. J. Math. Anal. Appl. 161 (1991), 388-394. MR 1132115 | Zbl 0753.34027
[8] Nieto J.J.: Nonlinear second order periodic boundary value problems with Carathéodory functions. Applicable Anal. 34 (1989), 111-128. MR 0926825 | Zbl 0662.34022
Partner of
EuDML logo