Existence and iteration of monotone positive solutions for an elastic beam equation with a corner

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 4, 2009, Pages 2097-2103

  Zhang, Xiaoping ^a  

^a ZHEJIANG UNIVERSITY OF MEDIA AND COMMUNICATIONS   (China)

Author keywords

Elastic beam equations; Existence; Monotone iterative method; Positive solutions

Indexed keywords

ELASTIC BEAM EQUATIONS; EXISTENCE; ITERATIVE SCHEMES; MONOTONE ITERATIVE METHOD; MONOTONE ITERATIVE TECHNIQUES; MONOTONE POSITIVE SOLUTIONS; POSITIVE SOLUTIONS;

ITERATIVE METHODS;

EID: 61749087765     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.03.017     Document Type: Article

References (19)

1. Agarwal R.P. On fourth-order boundary value problems arising in beam analysis. Differential Integral Equations 2 (1989) 91-110
2. B. Ahmad, J. Nieto, The monotone iterative technique for three-point second-order integrodifferential boundary value problems with p-Laplacian, Boundary Value Problems, vol. 2007, Article ID 57481, 9 pages, doi:10.1155/2007/57481
3. Bai Z. The upper and lower solution method for some fourth-order boundary value problems. Nonlinear Anal. 67 (2007) 1704-1709
4. Bai Z., and Wang H. On positive solutions of some nonlinear fourth-order beam equations. J. Math. Anal. Appl. 270 (2002) 357-368
5. Dalmasso R. Uniqueness of positive so1solutions for some nonlinear fourth order equations. J. Math. Anal. Appl. 201 (1996) 152-168
6. Ehme J., Eloe P.W., and Henderson J. Upper and lower solution methods for fully nonlinear boundary value problems. J. Differential Equations 180 (2001) 51-64
7. Graef J.R., and Yang B. Positive solutions of a nonlinear fourth order boundary value problem. Commun. Appl. Nonl. Anal. 14 1 (2007) 61-73
8. Graef J.R., and Yang B. Existence and nonexistence of positive solutions of fourth order nonlinear boundary value problems. Appl. Anal. 74 1-2 (2000) 201-214
9. Gupta C.P. Existence and uniqueness theorems for the bending of an elastic beam equation. Appl. Anal. 26 (1988) 289-304
10. Li Y. Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl. 281 (2003) 477-484
11. Li Y. Two-parameter nonresonance condition for the existence of fourth-order boundary value problems. J. Math. Anal. Appl. 308 (2005) 121-128
12. Liu B. Positive solutions of fourth-order two-point boundary value problems. Appl. Math. Comput. 148 (2004) 407-420
13. Ma D., Du Z., and Ge W. Existence and iteration of monotone positive solutions for multipoint boundary value problems with p-Laplacian operator. Comput. Math. Appl. 50 (2005) 729-739
14. Ma R., and Wang H. On the existence of positive solutions of fourth-order ordinary differential equations. Appl. Anal. 59 (1995) 225-231
15. Sun B., and Ge W. Successive iteration and positive pseudo-symmetric solutions for a three-point second-order p-Laplacian boundary value problems. Appl. Math. Comput. 188 2 (2007) 1772-1779
16. Yang B. Positive solutions for the beam equation under certain boundary value problems. Electron. J. Differential Equations 2005 78 (2005) 1-8
17. Yang B. Positive solutions for a fourth order boundary value problem. Electron. J. Qualitative Theory Diff. Equ. 2005 3 (2005) 1-17
18. Yao Q. Positive solutions for eigenvalue problems of fourth-order elastic beam equations. Appl. Math. Lett. 17 (2004) 237-243
19. Yao Q. Monotone iterative technique and positive solutions of Lidstone boundary value problems. Appl. Math. Comput. 138 (2003) 1-9