Existence and multiplicity of solutions of a kind of fourth-order boundary value problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 62, Issue 5, 2005, Pages 803-816

  Li, Fuyi ^a   Zhang, Qi ^a   Liang, Zhanping ^a  

^a SHANXI UNIVERSITY   (China)

Author keywords

Boundary value problem; Critical point theory; Mountain pass lemma; PS condition; Strongly monotone operator principle

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; GREEN'S FUNCTION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NONLINEAR SYSTEMS; PROBLEM SOLVING;

CRITICAL POINT THEORY; MOUNTAIN PASS LEMMA; PS CONDITION; STRONGLY MONOTONE OPERATOR PRINCIPLE;

BOUNDARY VALUE PROBLEMS;

EID: 21244497282     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.03.054     Document Type: Article

References (17)

1. Z. Bai, and H. Wang On positive solutions of some nonlinear fourth-order beam equations J. Math. Anal. Appl. 270 2002 357 368
2. J.M. Davis, P.W. Eloe, and J. Henderson Triple positive solutions and dependence on higher order derivatives J. Math. Anal. Appl. 237 1999 710 720
3. J.M. Davis, J. Henderson, and P.J.Y. Wong General Lidstone problems: multiplicity and symmetry of solutions J. Math. Anal. Appl. 251 2000 527 548
4. K. Deimling Nonlinear Functional Analysis 1985 Springer Berlin, Heidelberg
5. J.R. Graef, C. Qian, and B. Yang Multiple symmetric positive solutions of a class of boundary value problem for higher order ordinary differential equations Proc. Am. Math. Soc. 131 2003 577 585
6. D. Guo, Nonlinear Functional Analysis, second ed., Shandong Science & Technology Press, 2001 (in Chinese).
7. Y. Li Positive solutions of fourth-order periodic boundary value problems Nonlinear Anal. 54 2003 1069 1078
8. Y. Li Positive solutions of fourth-order boundary value problems with two parameters J. Math. Anal. Appl. 281 2003 477 484
9. B. Liu Positive solutions of fourth-order two point boundary value problems Appl. Math. Comput. 148 2004 407 420
10. P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1986.
11. M. Struwe Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems second ed. 1996 Springer Berlin, Heidelberg
12. A.E. Taylor, and D.C. Lay Introduction to Functional Analysis second ed. 1980 Wiley New York
13. Q. Yao Positive solutions for eigenvalue problems of fourth-order elastic beam equations Appl. Math. Lett. 17 2004 237 243
14. E. Zeidler Nonlinear Functional Analysis and its Applications, III: Variational Methods and Optimization 1985 Springer New York
15. E. Zeidler Nonlinear Functional Analysis and its Applications, I: Fixed-Point Theorems 1986 Springer New York
16. E. Zeidler Nonlinear Functional Analysis and its Applications, II/B: Nonlinear Monotone Operators 1990 Springer New York
17. B. Zhang, and X. Liu Existence of multiple symmetric positive solutions of higher order Lidstone problems J. Math. Anal. Appl. 284 2003 672 689