The method of lower and upper solutions for fourth order singular m-point boundary value problems

Journal of Mathematical Analysis and Applications

Volumn 322, Issue 2, 2006, Pages 675-692

  Wei, Zhongli ^a,b   Pang, Changci ^a,b  

^a SHANDONG JIANZHU UNIVERSITY   (China)

^b SHANDONG UNIVERSITY   (China)

Author keywords

Comparison theorem; Lower and upper solution; Partial ordering; Positive solution; Singular m point boundary value problem

Indexed keywords

EID: 33747034225     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.09.064     Document Type: Article

References (21)

1. O'Regan D. Theory of Singular Boundary Value Problems (1994), World Scientific, Singapore
2. Taliaferro S.D. A nonlinear singular boundary value problem. Nonlinear Anal. 3 (1979) 897-904
3. Zhang Y. Positive solutions of singular sub-linear Emden-Fowler boundary value problems. J. Math. Anal. Appl. 185 (1994) 215-222
4. O'Regan D. Singular Dirichlet boundary value problems-I. Super-linear and non-resonance case. Nonlinear Anal. 29 2 (1997) 221-245
5. Wei Z., and Pang C. Positive solutions of non-resonant singular boundary value problem of second order differential equations. Nagoya Math. J. 162 (2001) 127-148
6. Feng W., and Webb J.R.L. Solvability of a m-point boundary value problems with nonlinear growth. J. Math. Anal. Appl. 212 (1997) 467-480
7. Gupta C.P. Solvability of a three-point boundary value problems for a second order ordinary differential equation. J. Math. Anal. Appl. 168 (1992) 540-551
8. Gupta C.P. A generalized multi-point boundary value problem for second order ordinary differential equations. Appl. Math. Comput. 89 (1998) 133-146
9. Ma R. Positive solutions of a nonlinear three-point boundary value problem. Electron. J. Differential Equations 34 (1999) 1-8
10. Ma R. Existence of solution of nonlinear m-point boundary value problem. J. Math. Anal. Appl. 256 (2001) 556-567
11. Xu X. Positive solutions for singular m-point boundary value problems with positive parameter. J. Math. Anal. Appl. 291 (2004) 352-367
12. Xu X. Multiplicity results for positive solutions of some semi-positone three-point boundary value problems. J. Math. Anal. Appl. 291 (2004) 673-689
13. Zhang G., and Sun J. Positive solutions of m-point boundary value problems. J. Math. Anal. Appl. 291 (2004) 406-418
14. Zhang Z., 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 (2002) 41-52
15. Schroder J. Fourth order two-point boundary value problems estimates by two-sided bounds. Nonlinear Anal. 8 2 (1984) 107-114
16. Gupta C.P. Existence and uniqueness results for the bending of an elastic beam equation at resonance. J. Math. Anal. Appl. 135 (1988) 208-225
17. Aftabizadeh A.R. Existence and uniqueness theorems for fourth order boundary value problems. J. Math. Anal. Appl. 116 (1986) 415-426
18. Usmani R.A. A uniqueness theorem for a boundary value problem. Proc. Amer. Math. Soc. 77 (1979) 329-335
19. O'Regan D. Solvability of some fourth (and higher) order singular boundary value problems. J. Math. Anal. Appl. 161 (1991) 78-116
20. Hartman P. Ordinary Differential Equations. second ed. (1982), Birkhäuser, Boston
21. Wei Z. A class of fourth order singular boundary value problems. Appl. Math. Comput. 153 3 (2004) 865-884