Third-order nonlocal problems with sign-changing nonlinearity on time scales

Electronic Journal of Differential Equations

Volumn 2007, Issue , 2007, Pages 1-12

  Anderson, Douglas R ^a   Tisdell, Christopher C ^b  

^a and Exercise Science   (United States)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Boundary value problem; Green's function; Three point; Time scale

Indexed keywords

EID: 33846703346     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. D.R. Anderson, Multiple positive solutions for a three point boundary value problem, Math. Comput. Model., 27 (1998) 49-57.
2. D.R. Anderson, Discrete third-order three-point right focal boundary value problems, Comput. Math. Appl., 45 (2003) 861-871.
3. D.R. Anderson and A. Cabada, Third-order right-focal multi-point problems on time scales, J. Differ. Equations Appl., 12:9 (2006) 919-935.
4. D.R. Anderson and J.M. Davis, Multiple solutions and eigenvalues for third-order right focal boundary value problems, J. Math. Anal. Appl., 267:1 (2002) 135-157.
5. F.M. Atici and G.Sh. Guseinov, On Green's functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math. 141 (2002) 75-99.
6. M. Bohner and H. Luo, Singular second-order multipoint dynamic boundary value problems with mixed derivatives, Adv. Differ. Eq., 2006: 15 pages, Article ID 54989 (2006).
7. M. Bohner and A. Peterson, editors, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
8. J.M. Davis, L.H. Erbe, and J. Henderson, Multiplicity of positive solutions for higher order Sturm-Liouville problems, Rocky Mountain J. Math., 31 (2001) 169-184.
9. P.W. Eloe and J. McKelvey, Positive solutions of three point boundary value problems, Comm. Appl. Nonlinear Anal., 4 (1997) 45-54.
10. L.H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120 (1994) 743-748.
11. I.M. Gamba and A. Jüngel, Positive solutions to singular second and third order differential equations for quantum fluids, Archive for Rational Mechanics and Analysis 156:3 (2001) 183-203.
12. J.R. Graef and B. Yang, Multiple positive solutions to a three point third order boundary value problem, Discrete and Continuous Dynamical Systems, Supplement Volume (2005) 1-8.
13. J.R. Graef and B. Yang, Positive solutions of a nonlinear third order eigenvalue problem, Dynamic Sys. Appl., 15 (2006) 97-110.
14. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988.
15. J. Henderson, Multiple solutions for 2mth order Sturm-Liouville boundary value problems on a measure chain, J. Differ. Equations Appl., 6 (2000) 417-429.
16. J. Henderson, Double solutions of impulsive dynamic boundary value problems on a time scale, J. Diff. Equations Appl., 8:4 (2002) 345-356.
17. J. Henderson and H.B. Thompson, Existence of multiple solutions for second order boundary value problems, J. Differential Equations, 166 (2000) 443-454.
18. W. Kelley and A. Peterson, The Theory of Differential Equations: Classical and Qualitative, Pearson/Prentice Hall (2004) Upper Saddle River, NJ.
19. K.Q. Lan, Multiple positive solutions of semilinear differential equations with singularities, J. London Math. Soc., 63 (2001) 690-704.
20. K.Q. Lan, Multiple positive solutions of semi-positone Sturm-Liouville boundary value problems, Bull. London Math. Soc. 38 (2006) 283-293.
21. D.X. Ma, Z.J. Du, and W.G. Ge, Existence and iteration of monotone positive solutions for multipoint boundary value problem with p-Laplacian operator, Comput. Math. Appl., 50 (2005) 729-739.
22. R. Ma and B. Thompson, Positive solutions for nonlinear m-point eigenvalue problems, J. Math. Anal. Appl., 297 (2004) 24-37.
23. Y.P. Sun, Positive solutions of singular third-order three-point boundary value problem, J. Math. Anal. Appl., 306 (2005) 589-603.
24. C.C. Tisdell, P. Drábek, and J. Henderson, Multiple solutions to dynamic equations on time scales, Comm. Appl. Nonlinear Anal. 11:4 (2004) 25-42.
25. P.J.Y. Wong, Eigenvalue characterization for a system of third-order generalized right focal problems, Dynamic Sys. Appl., 15 (2006) 173-192.
26. X.G. Zhang, H.C. Zou, and L.S. Liu, Positive solutions of second order m-point boundary value problems with changing sign singular nonlinearity, Appl. Math. Lett., (2006) doi:10.1016/j.aml.2006.08.005.