Existence and multiplicity of solutions for fourth-order boundary value problems with parameters

Journal of Mathematical Analysis and Applications

Volumn 327, Issue 1, 2007, Pages 362-375

  Liu, Xi Lan ^a   Li, Wan Tong ^b  

^a Department of Mathematics   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Existence; Fourth order BVP; Multiple solutions

Indexed keywords

EID: 33750834865     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.04.021     Document Type: Article

References (29)

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. On fourth order boundary value problems arising in beam analysis. Differential Integral Equations 2 (1989) 91-110
3. Agarwal R.P., and Wilson S.J. On a fourth order boundary value problem. Util. Math. 26 (1984) 297-310
4. Agarwal R.P., and Chow Y.M. Iterative methods for a fourth order boundary value problem. J. Comput. Appl. Math. 10 (1984) 203-217
5. Anello G. A multiplicity theorem for critical points of functionals on reflexive Banach spaces. Arch. Math. 82 (2004) 172-179
6. Bai Z. The method of lower and upper solutions for a bending of a elastic beam equation. J. Math. Anal. Appl. 248 (2000) 195-202
7. Bai Z., and Wang H. On positive solutions of some nonlinear fourth-order beam equations. J. Math. Anal. Appl. 270 (2002) 357-368
8. Bonanno G. Some remarks on a three critical points theorem. Nonlinear Anal. TMA 54 (2003) 651-665
9. Chen W.Y. A decomposition problem for operators. Xuebao of Dongbei Renmin University 1 (1957) 95-98 (in Chinese)
10. Davis J.M., Henderson J., and Wong P.J.Y. General Lidstone problems: Multiplicity and symmetry of solutions. J. Math. Anal. Appl. 251 (2000) 527-548
11. Guo D. Nonlinear Functional Analysis (2001), Shandong Science and Technology Press (in Chinese)
12. Gupta C.P. Existence and uniqueness theorems for a bending of an elastic beam equation. Appl. Anal. 26 (1988) 289-304
13. Hao Z.C., and Debnath L. On eigenvalue intervals and eigenfunctions of fourth-order singular boundary value problems. Appl. Math. Lett. 18 (2005) 543-553
14. Liu B. Positive solutions of fourth-order two point boundary value problems. Appl. Math. Comput. 148 (2004) 407-500
15. Li F., Zhang Q., and Liang Z. Existence and multiplicity of solutions of a kind of fourth-order boundary value problem. Nonlinear Anal. 62 (2005) 803-816
16. Li Y. Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl. 281 (2003) 477-484
17. Li Y. Two parameter nonresonance condition for the existence of fourth-order boundary value problems. J. Math. Anal. Appl. 308 (2005) 121-138
18. Li Y. Positive solutions of fourth-order periodic boundary value problems. Nonlinear Anal. TMA 54 (2003) 1069-1078
19. Liu Y.S. Multiple positive solutions to fourth-order singular boundary value problems in abstract space. Electron. J. Differential Equations 2004 120 (2004) 1-13
20. Liu X.L., and Li W.T. Positive solutions of the nonlinear fourth-order beam equation with three parameters. J. Math. Anal. Appl. 303 (2005) 150-163
21. X.L. Liu, W.T. Li, Positive solutions of the nonlinear fourth-order beam equation with three parameters (II), Dynam. Systems Appl., in press
22. Krasnosel'skii M. Topological Methods in the Theory of Nonlinear Integral Equations (1956), Gostehizdat, Moscow (in Russian) (Engl. transl., Pergamon Press, New York, 1964)
23. 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
24. Ricceri B. On a three critical points theorem. Arch. Math. 75 (2000) 220-226
25. Ricceri B. A general variational principle and some of its applications. J. Comput. Appl. Math. 113 (2000) 401-410
26. Willem M. Minimax Theorems (1996), Birkhäuser, Boston
27. Yao Q. On the positive solutions of a nonlinear fourth-order boundary value problem with two parameters. Appl. Anal. 83 (2004) 97-107
28. Yao Q. Existence, multiplicity and infinite solvability of positive solutions to a nonlinear fourth-order periodic boundary value problem. Nonlinear Anal. TMA 63 (2005) 237-246
29. Yang Y.S. Fourth-order two-point boundary value problems. Proc. Amer. Math. Soc. 104 1 (1988) 175-180