Solutions of second order multi-point boundary value problems

Mathematical Proceedings of the Cambridge Philosophical Society

Volumn 145, Issue 2, 2008, Pages 489-510

  Graef, John R ^a   Kong, Lingju ^a  

^a UNIVERSITY OF TENNESSEE AT CHATTANOOGA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49549100886     PISSN: 03050041     EISSN: 14698064     Source Type: Journal    
DOI: 10.1017/S0305004108001424     Document Type: Article

References (22)

1. D. R. ANDERSON and R. I. AVERY. A fourth-order four-point right focal boundary value problem. Rocky Mountain J. Math. 36 (2006), 367-380.
2. R. I. AVERY and J. HENDERSON. Three symmetric positive solutions for a second-order boundary value problem. Appl. Math. Lett. 13 (2000), 1-7
3. K. DEIMLING. Nonlinear Functional Analysis (Spring-Verlag, 1985).
4. L. ERBE. Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems. Math. Comput. Model. 32 (2000), 529-539.
5. D. GUO and V. LAKSHMIKANTHAM. Nonlinear Problems in Abstract Cones (Academic Press, 1988).
6. J. R. GRAEF and L. KONG. Necessary and sufficient conditions for the existence of symmetric positive solutions of multi-point boundary value problems. Nonlinear Anal. 68 (2008), 1529-1552.
7. J. R. GRAEF, L. KONG and Q. KONG. Symmetric positive solutions of nonlinear boundary value problems. J. Math. Anal. Appl. 326 (2007), 1310-1327.
8. J. R. GRAEF, C. QIAN and B. YANG. Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations. Proc. Amer. Math. Soc. 131 (2003), 577-585.
9. X. HAN. Positive solutions for a three-point boundary value problem. Nonlinear Anal. 66 (2007), 679-688.
10. J. HENDERSON. Solutions of multipoint boundary value problems for second order equations. Dynam. Systems Appl. 15 (2006), 111-117.
11. J. HENDERSON and H. B. THOMPSON. Multiple symmetric positive solutions for a second order boundary value problem. Proc. Amer. Math. Soc. 128 (2000), 2373-2379.
12. L. KONG and Q. KONG. Second-order boundary value problems with nonhomogeneous boundary condition (I). Math. Nachr. 278 (2005), 173-193.
13. Q. KONG. Existence and nonexistence of solutions of second-order nonlinear boundary value problems. Nonlinear Anal. 66 (2007), 2635-2651.
14. R. MA. Existence of positive solutions for superlinear semipositone m-point boundary value problems. Proc. Edinburgh Math. Soc. 46 (2003), 279-292.
15. R. MA and D. O'REGAN. Nodal solutions for second-order m-point boundary value problems with nonlinearities across several eigenvalues. Nonlinear Anal. 64 (2006), 1562-1577.
16. J. SUN and G. ZHANG. Nontrivial solutions of singular sublinear Sturm-Liouville problems. J. Math. Anal. Appl. 326 (2007), 242-251.
17. Y. SUN. Optimal existence criteria for symmetric positive solutions to a three-point boundary value problem. Nonlinear Anal. 66 (2007), 1051-1063.
18. C. SWARTZ. An Introduction to Functional Analysis (Marcel Dekker, 1992).
19. J. R. L. WEBB. Optimal constants in a nonlocal boundary value problem. Nonlinear Anal. 63 (2005), 672-685.
20. J. R. L. WEBB and K. Q. LAN. Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topol. Methods Nonlinear Anal. 27 (2006), 91-115.
21. E. ZEIDLER. Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems (Springer-Verlag, 1986).
22. G. ZHANG and J. SUN. Positive solutions of m-point boundary value problems. J. Math. Anal. Appl. 291 (2004), 406-418.