A monotone method for constructing extremal solutions to fourth-order periodic boundary value problems

Applied Mathematics and Computation

Volumn 132, Issue 2-3, 2002, Pages 411-421

  Jiang, Daqing ^a   Gao, Wenjie ^b   Wan, Aying ^c  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b JILIN UNIVERSITY   (China)

^c Hulunbeir College   (China)

Author keywords

Existence; Monotone iterative technique; Periodic boundary value problem; Upper and lower solutions

Indexed keywords

EID: 0037058264     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(01)00201-6     Document Type: Article

References (16)

1. A.R. Aftabizadeh Existence and uniqueness theorems for fourth-order boundary value problems J. Math. Anal. Appl. 116 1986 415 426
2. C.P. Gupta Existence and uniqueness results for some fourth order fully quasilinear boundary value problems Anal. Appl. 36 1990 169 175
3. C.P. Gupta Existence and uniqueness results for a bending of an elastic beam equation at resonance J. Math. Anal. Appl. 135 1988 208 225
4. C.P. Gupta Existence and uniqueness theorem for a bending of an elastic beam equation Anal. Appl. 26 1988 289 304
5. R.A. Usmani A uniqueness theorem for a boundary value problem Proc. Amer. Math. Soc. 77 1979 327 335
6. Y. Yang Fourth-order two-point boundary value problem Proc. Amer. Math. Soc. 104 1988 175 180
7. V. Seda J.J. Nieto M. Gera Periodic boundary value problems for nonlinear higher order ordinary differential equations Appl. Math. Comput. 48 1992 71 82
8. C. De Coster L. Sanchez Upper and lower solutions, Ambrosetti–Prodi problems and positive solutions for fourth order O.D.E. Riv. Mat. Pural Appl. 14 1994 1129 1138
9. D. Dunninger Existence of positive solutions for fourth-order nonlinear problems Boll. Un. Mat. Ital. 7 1987 1129 1138
10. P. Korman A maximum principle for fourth-order ordinary differential equations Appl. Anal. 33 1989 267 273
11. F. Sadyrabaev Two-point boundary value problems for fourth-order Acta Univ. Latviensis 553 1990 84 91
12. J. Schroder Fourth-order two-point boundary value problems; estimates by two side bounds Nonlinear Anal. 8 1984 107 114
13. A. Cabada The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems J. Math. Anal. Appl. 185 1994 302 320
14. H.Z. Wang Periodic solutions of four-order differential equations Acta Sci. Nat. Un Jilinensis 4 1993 415 422 (in Chinese)
15. R.Y. Ma J.H. Zhang S.M. Fu The method of lower and upper solutions for fourth-order two-point boundary value problems J. Math. Anal. Appl. 215 1997 415 422
16. G.S. Ladde V. Lakshmikantham A.S. Vatsala Monotone Iterative Techniques for Nonlinear Differential Equations 1985 Pitman Boston, MA