Existence of positive solutions for fourth-order m-point boundary value problem with variable parameters

Applied Mathematics and Computation

Volumn 190, Issue 2, 2007, Pages 1417-1431

  Zhang, Mingchuan ^a   Wei, Zhongli ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Fixed point index; Fourth order m point BVP; Positive solution; Variable parameter

Indexed keywords

NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PROBLEM SOLVING; THEOREM PROVING;

FIXED POINT INDEX; POSITIVE SOLUTION; VARIABLE PARAMETERS;

BOUNDARY VALUE PROBLEMS;

EID: 34250624453     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.02.019     Document Type: Article

References (19)

1. Il'in V.A., and Moiseev E.I. Nonlocal boundary value problem of the first kind for a Sturm-CLiouville operator in its differential and finite difference aspects. Differen. Equat. 23 (1987) 803-810
2. Gupta C.P. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. J. Math. Anal. Appl. 168 (1992) 540-551
3. Gupta C.P. Existence and uniqueness theorem for a bending of an elastic beam equation. Anal. Appl. 26 (1988) 289-304
4. Gupta C.P. A generalized multi-point boundary value problem for second order ordinary differential equations. Appl. Math. Comput. 89 (1998) 133-146
5. 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
6. Jiang D., Liu H., and Xu X. Nonresonant singular fourth-order boundary value problems. Appl. Math. Lett. 18 (2005) 69-75
7. Ma R. Positive solutions of a nonlinear three-point boundary-value problems. Electron. J. Differen. Equat. 34 (1999) 1-8
8. Ma R. Existence of solutions of nonlinear m-point boundary value problem. J. Math. Anal. Appl. 256 (2001) 556-567
9. Webb J.R.L. Positive solutions of some three-point boundary value problems via fixed point theory. Nonlinear Anal. 47 (2001) 4319-4332
10. Ma H. Positive solution for m-point boundary value problems of fourth order. J. Math. Anal. Appl. 321 (2006) 37-49
11. Chai G. Existence of positive solutions for fourth-order boundary value problem with variable parameters. Nonlinear Anal. 66 (2007) 870-880
12. Li Y. Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl. 281 (2003) 477-484
13. Moshinsky M. Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas. Bol. Soc. Mat. Mexicana 7 (1950) 1-25
14. Timoshenko S. Theory of Elastic Stability (1961), McGraw-Hill, New York
15. Ma R. Positive solutions for nonlinear m-point eigenvalue problems. J. Math. Anal. Appl. 297 (2004) 24-37
16. Guo D., and Lakskmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, New York
17. Yao Q. On the positive solutions of a nonlinear fourth-order boundary value problem. Appl. Anal. 83 (2004) 97-107
18. Yao Q. Positive solutions for eigenvalue problems of fourth-order elastic beam equations. Appl. Math. Lett. 17 (2004) 237-243
19. Pang C., and Wei Z. Positive solutions and multiplicity of fourth-order boundary value problems with two parameters. Acta Math. Sinica 3 (2006) 625-632 (in Chinese)