Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
periodic solution; maximum principle; upper and lower solutions; monotone method
periodic solution; maximum principle; upper and lower solutions; monotone method
Summary:
In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.
References:
[1] Aftabizadeh A.R., Gupta C.P., Xu J.M.: Existence and uniqueness theorems for three-point boundary value problems. SIAM J. Math. Anal. 20 (1989), 716-726. MR 0990873 | Zbl 0704.34019
[2] Aftabizadeh A.R., Gupta C.P., Xu J.M.: Periodic boundary value problems for third order ordinary differential equations. Nonlinear Anal. 14 (1990), 1-10. MR 1028242 | Zbl 0706.34018
[3] Afuwape A.U., Omari P., Zanolin F.: Nonlinear perturbations of differential operators with nontrivial kernel and applications to third-order periodic boundary value problems. J. Math. Anal. Appl. 143 (1989), 35-56. MR 1019448 | Zbl 0695.47044
[4] Afuwape A.U., Zanolin F.: An existence theorem for periodic solutions and applications to some third order nonlinear differential equations. preprint.
[5] Agarwal R.P.: Boundary Value Problems for Higher Order Differential Equations. World Scientific, Singapore, 1986. MR 1021979 | Zbl 0921.34021
[6] Agarwal R.P.: Existence-uniqueness and iterative methods for third-order boundary value problems. J. Comp. Appl. Math. 17 (1987), 271-289. MR 0883170 | Zbl 0617.34008
[7] 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
[8] Ezeilo J.O.C., Nkashama M.N.: Resonant and nonresonant oscillations for some third order nonlinear ordinary differential equations. Nonlinear Anal. 12 (1988), 1029-1046. MR 0962767 | Zbl 0676.34021
[9] Gregus M.: Third Order Linear Differential Equations. D. Reidel, Dordrecht, 1987. MR 0882545 | Zbl 0602.34005
[10] Ladde G.S., Lakshmikantham V., Vatsala A.S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston, 1985. MR 0855240 | Zbl 0658.35003
[11] Lakshmikantham V., Nieto J.J., Sun Y.: An existence result about periodic boundary value problems of second order differential equations. Appl. Anal., to appear. MR 1121320
[12] Nieto J.J.: Nonlinear second order periodic boundary value problems. J. Math. Anal. Appl. 130 (1988), 22-29. MR 0926825 | Zbl 0678.34022
[13] Rudolf B., Kubacek Z.: Remarks on J. J. Nieto's paper: Nonlinear second order periodic boundary value problems. J. Math. Anal. Appl. 146 (1990), 203-206. MR 1041210 | Zbl 0713.34015
[14] Temam R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York, 1988. MR 0953967 | Zbl 0871.35001
Search
Partner of
