Existence of at least three solutions of a second-order three-point boundary value problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 64, Issue 6, 2006, Pages 1356-1366

  Khan, Rahmat Ali ^a   Webb, J R L ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Multiple solutions; Three point boundary conditions; Topological degree; Upper and lower solutions

Indexed keywords

NONLINEAR SYSTEMS; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

MULTIPLE SOLUTIONS; THREE-POINT BOUNDARY CONDITIONS; TOPOLOGICAL DEGREE; UPPER AND LOWER SOLUTIONS;

BOUNDARY VALUE PROBLEMS;

EID: 30944433189     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.06.040     Document Type: Article

References (16)

1. Z. Bai, W. Ge, and Y. Wang Multiplicity results for some second-order four-point boundary-value problems Nonlinear Anal. 60 2005 491 500
2. S.R. Bernfeld, and V. Lakshmikantham An Introduction to Nonlinear Boundary Value Problems 1974 Academic Press New York, London
3. C. Fabry, J. Mawhin, and M.N. Nkashama A multiplicity result for periodic solutions of forced nonlinear second order differential equations Bull. London Math. Soc. 18 1986 173 180
4. K. Goudreau A multiplicity result for a nonlinear boundary value problem J. Math. Anal. Appl. 218 1998 395 408
5. Y. Guo, and W. Ge Positive solutions for three-point boundary value problems with dependence on the first derivative J. Math. Anal. Appl. 290 2004 291 301
6. C.P. Gupta Solvability of a three-point boundary value problem for a second order ordinary differential equation J. Math. Anal. Appl. 168 1992 540 551
7. J. Henderson, and H.B. Thompson Existence of multiple solutions for second order boundary value problems J. Differential Equations 166 2000 443 454
8. R.A. Khan, J.R.L. Webb, Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth, submitted for publication.
9. R.W. Leggett, and L.R. Williams Multiple positive fixed points of nonlinear operators on ordered Banach spaces Indiana Univ. Math. J. 28 1979 673 688
10. R. Ma, and H. Wang Positive solutions of a nonlinear three-point boundary value problems J. Math. Anal. Appl. 279 2003 216 227
11. M.N. Nkashama A generalized upper and lower solutions method and multiplicity results for periodic solutions of nonlinear first order differential equations J. Math. Anal. Appl. 140 1989 381 395
12. I. Rachunkova Multiplicity results for four point boundary value problems Nonlinear Anal. 18 1992 497 505
13. J.-P. Sun, W.-T. Li, and Y.-H. Zhao Three positive solutions of a nonlinear three-point boundary value problem J. Math. Anal. Appl. 288 2003 708 716
14. J.R.L. Webb Positive solutions of some three point boundary value problems via fixed point index theory Nonlinear Anal. 47 2001 4319 4332
15. X. Xu Multiplicity results for positive solutions of some semi-positone three-point boundary value problems J. Math. Anal. Appl. 291 2004 673 689
16. Zengji Du, Chunyan Xue, Weigao Ge, Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative, Arch. Math. 84 (2005) 341-349.