Upper and lower solution method for fourth-order four-point boundary value problems

Journal of Computational and Applied Mathematics

Volumn 196, Issue 2, 2006, Pages 387-393

  Zhang, Qin ^a   Chen, Shihua ^a   Lü, Jinhu ^b  

^a WUHAN UNIVERSITY   (China)

^b INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Four point boundary conditions; Fourth order ordinary differential equation; Lower and upper solution method

Indexed keywords

BOUNDARY CONDITIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

FOUR-POINT BOUNDARY CONDITIONS; FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATION; LOWER AND UPPER SOLUTION METHOD; NONNEGATIVE CONSTANTS;

BOUNDARY VALUE PROBLEMS;

EID: 33746239224     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.09.007     Document Type: Article

References (14)

1. Aftabizadeh A.R. Existence and uniqueness theorems for fourth-order boundary value problems. J. Math. Anal. Appl. 116 (1986) 415-426
2. Agarwal R.P. Focal Boundary Value Problems for Differential and Difference Equations (1998), Kluwer Academic, Dordrecht
3. Del Pino M.A., and Manasevich R.F. Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition. Proc. Amer. Math. Soc. 112 (1991) 81-86
4. Graef J.R., and Yang B. On a nonlinear boundary value problem for fourth order equations. Appl. Anal. 72 (1999) 439-448
5. Hartman P. Ordinary Differential Equations (1982), Birkhäuser, Boston
6. Leela S. Monotone method for second order periodic boundary value problems. Nonlinear Anal. 7 (1983) 349-355
7. Ma T.F. Existence results and numerical solutions for a beam equation with nonlinear boundary conditions. Appl. Numer. Math. 47 (2003) 189-196
8. Ma R.Y., Zhang J.H., and Fu S.M. The method of lower and upper solutions for fourth-order two-point boundary value problems. J. Math. Anal. Appl. 215 (1997) 415-422
9. Rachunkova I. Upper and lower solutions and topological degree. J. Math. Anal. Appl. 234 (1999) 311-327
10. Shanthi V., and Ramanujam N. A numerical method for boundary value problems for singularly perturbed fourth-order ordinary differential equations. Appl. Math. Comput. 129 (2002) 269-294
11. Wong P.J.Y. Triple positive solutions of conjugate boundary value problems. Comput. Math. Appl. 36 (1998) 19-35
12. Yang Y. Fourth-order two-point boundary value problem. Proc. Amer. Math. Soc. 104 (1988) 175-180
13. Zhang Z.X., and Wang J. The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems. J. Comput. Appl. Math. 147 (2003) 41-52
14. Zill D.G., and Cullen M.R. Differential Equations with Boundary-value Problems. fifth ed. (2001), Brooks, Cole