Optimal existence criteria for symmetric positive solutions to a three-point boundary value problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 5, 2007, Pages 1051-1063

  Sun, Yongping ^a  

^a Hangzhou Radio & TV University   (China)

Author keywords

Fixed point index; Optimal existence; Symmetric positive solution; Three point boundary value problem

Indexed keywords

BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; THEOREM PROVING;

FIXED POINT INDEX; OPTIMAL EXISTENCE; SYMMETRIC POSITIVE SOLUTION; THREE-POINT BOUNDARY VALUE PROBLEM;

NONLINEAR EQUATIONS;

EID: 33845321039     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.01.004     Document Type: Article

References (27)

1. Avery R.I., and Peterson A.C. Three positive fixed points of nonlinear operators on ordered Banach spaces. Comput. Math. Appl. 42 (2001) 313-322
2. Deimling K. Nonlinear Functional Analysis (1985), Springer, Berlin
3. Feng W., and Webb J.R.L. Solvability of a three-point boundary value problems at resonance. Nonlinear Anal. 30 (1997) 3227-3238
4. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, Orlando
5. Guo D., and Sun J. Nonlinear Integral Equations (1987), Shandong Science and Technology Press, Jinan (in Chinese)
6. Gupta C.P. A shaper condition for the solvability of a three-point second order boundary value problem. J. Math. Anal. Appl. 205 (1997) 586-597
7. Gupta C.P. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations. J. Math. Anal. Appl. 168 (1992) 540-551
8. He X., and Ge W. Triple solutions for second-order three-point boundary value problems. J. Math. Anal. Appl. 268 (2002) 256-265
9. Henderson J., and Thompson H.B. Multiple symmetric positive solutions for a second order boundary value problem. Proc. Amer. Math. Soc. 128 (2000) 2373-2379
10. Infante G. Eigenvalues of some non-local boundary value problems. Proc. Edinb. Math. Soc. 46 (2003) 75-86
11. Infante G., and Webb J.R.L. Nonzero solutions of Hammerstein integral equations with discontinuous kernels. J. Math. Anal. Appl. 272 (2002) 30-42
12. Kosmatov N. Symmetric solutions of a multi-point boundary value problem. J. Math. Anal. Appl. 309 (2005) 25-36
13. Krein M.G., and Rutman M.A. Linear operators leaving invariant a cone in a Banach space. Amer. Math. Soc. Translations 10 (1950) 1-128
14. Li F., and Zhang Y. Multiple symmetric nonnegative solutions of second-order ordinary differential equations. Appl. Math. Lett. 17 (2004) 261-267
15. Liu B. Positive solutions of a nonlinear three-point boundary value problem. Comput. Math. Appl. 44 (2002) 201-211
16. Liu B. Positive solutions of a nonlinear three-point boundary value problem. Appl. Math. Comput. 132 (2002) 11-28
17. Ma R. Multiplicity results for a three-point boundary value problem at resonance. Nonlinear Anal. 53 (2003) 777-789
18. Ma R. Positive solutions of a nonlinear three-point boundary value problems. Electron. J. Differential Equations 34 (1999) 1-8
19. Ma R. Positive solutions for second-order three-point boundary value problems. Appl. Math. Lett. 14 (2001) 1-5
20. Ma R., and Thompson B. Global behavior of positive solutions of nonlinear three-point boundary value problems. Nonlinear Anal. 60 (2005) 685-701
21. Martin R.H. Nonlinear Operators and Differential Equations in Banach Spaces (1976), Wiley, New York
22. Webb J.R.L. Multiple positive solutions of some nonlinear heat flow problems. Discrete Contin. Dyn. Syst. Suppl (2005) 1-9
23. Webb J.R.L. Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Anal. 47 (2001) 4319-4332
24. Sun Y. Nontrivial solution for a three-point boundary value problem. Electron. J. Differential Equations 111 (2004) 1-10
25. Sun Y., and Liu L. Solvability for a nonlinear second-order three-point boundary value problem. J. Math. Anal. Appl. 296 (2004) 265-275
26. Xu X. Three solutions for three-point boundary value problems. Nonlinear Anal. 62 (2005) 1053-1066
27. Yao Q. Existence and iteration of n symmetric positive solutions for a singular two-point boundary value problem. Comput. Math. Appl. 47 (2004) 1195-1200