Upper and lower solution method for a fourth-order four-point boundary value problem on time scales

Applied Mathematics and Computation

Volumn 215, Issue 6, 2009, Pages 2243-2247

  Pang, Yuanyuan ^a   Bai, Zhanbing ^a  

^a SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Boundary value problem; Lower and upper solution method; Time scales

Indexed keywords

FOUR-POINT BOUNDARY VALUE PROBLEM; FOURTH-ORDER; LOWER AND UPPER SOLUTION METHOD; MONOTONE ITERATIVE TECHNIQUES; ON TIME; TIME SCALES; UPPER AND LOWER SOLUTIONS;

BOUNDARY VALUE PROBLEMS;

TIME MEASUREMENT;

EID: 70349988795     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.08.019     Document Type: Article

References (15)

1. Hilger S. Analysis on measure chains - a unified approach to continuous and discrete calculus. Results Math. 4 (1990) 18-56
2. Avery R.I., and Anderson D.R. Existence of three positive solutions to a second order BVP on a measure chain. J. Comput. Appl. Math. 141 (2002) 65-73
3. Bai Z.B., and Ge W.G. Existence of three positive solutions for some second order boundary-value problems. Comput. Math. Appl. 48 (2004) 699-707
4. Bai Z.B., Ge W.G., and Wang Y.F. Multiplicity results for some second-order four-point boundary-value problems. Nonlinear Anal. 60 (2005) 491-500
5. Ma R.Y., and Luo H. Existence of solutions for a two-point boundary value problem on time scales. Appl. Math. Comput. 150 (2004) 139-147
6. Bai Z.B., Liang X.Q., and Du Z.J. Triple positive solutions for some second-order boundary value problem on a measure chain. Comput. Math. Appl. 53 (2007) 1832-1839
7. Bai Z.B. The upper and lower solution method for some fourth-order boundary value problems. Nonlinear Anal. 67 (2007) 1704-1709
8. Feng H.Y., Ji D.H., and Ge W.G. Existence and uniqueness of solutions for a fourth-order boundary value problem. Nonlinear Anal. 70 (2009) 3561-3566
9. Liu B. Positive solutions of fourth-order two point boundary value problems. Appl. Math. Comput. 148 (2004) 407-420
10. Wang D.B., and Sun J.P. Existence of a solution and a positive solution of a boundary value problem for a nonlinear fourth-order dynamic equation. Nonlinear Anal. 69 (2008) 1817-1823
11. Chen S.H., Ni W., and Wang C.P. Positive solution of fourth order ordinary differential equation with four-point boundary conditions. Appl. Math. Lett. 19 (2006) 161-168
12. Agarwal R.P., Bohner M., ORegan D., and Peterson A. Dynamic equations on time scales: a survey. J. Comput. Appl. Math. 141 (2002) 1-26
13. Agarwal R.P., and ORegan D. Nonlinear boundary value problems on time scales. Nonlinear Anal. 44 (2001) 527-535
14. Aulbach B., and Neidhart L. Integration on measure chains. Proceedings of the Sixth International Conference on Difference Equations (2004), CRC, Boca Raton, FL 239-252
15. Agarwal R.P., Bohner M., and Rehak P. Half-linear dynamic equations. Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th Birthday vol. 1 (2003), Kluwer Academic Publishers, Dordrecht 1-57