Existence of multiple positive solutions for m-point boundary value problems in Banach spaces

Journal of Computational and Applied Mathematics

Volumn 215, Issue 1, 2008, Pages 79-90

  Zhao, Yu Lin ^a,b   Chen, Hai Bo ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b HUNAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Banach spaces; Boundary value problem; Positive solutions; Strict set contractions

Indexed keywords

BANACH SPACES; NONLINEAR ANALYSIS; SET THEORY; THEOREM PROVING;

POSITIVE SOLUTIONS; STRICT-SET-CONTRACTIONS;

BOUNDARY VALUE PROBLEMS;

EID: 39849107906     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2007.03.025     Document Type: Article

References (16)

1. Cac N.P., and Gatica J.A. Fixed point theorems for mapping in ordered Banach space. J. Math. Anal. Appl. 71 (1979) 545-557
2. Chen S.H., Hu T., Chen L., et al. Existence results for n-point boundary value problem of second order ordinary differential equations. J. Comput. Appl. Math. 180 (2005) 425-432
3. Demling K. Ordinary Differential Equations in Banach Spaces (1977), Springer, Berlin
4. Feng W., and Weeb T.R.L. Solvability of a m-point boundary value problem with nonlinear growth. J. Math. Anal. Appl. 212 (1997) 467-480
5. Guo D., and Lakshmikantham V. Nonlinear Problems in Abstract Cones (1988), Academic Press, San Diego
6. Guo D., and Lakshmikantham V. Multiple solutions of two-point boundary value problem of ordinary differential equations in Banach space. J. Math. Anal. Appl. 129 (1988) 211-222
7. Guo D., Lakshmikantham V., and Liu X. Nonlinear Integral Equation in Abstract Spaces (1996), Kluwer Academic Publishers, Dordrecht
8. Guo Y., Shan W., and Ge W. Positive solutions for a second order m-point boundary value problem. J. Comput. Appl. Math. 151 (2003) 415-424
9. Gupta C.P. A generalized multi-point boundary value problem for second kind for a Sturm-Liouville operator. Appl. Math. Comput. 89 (1998) 133-146
10. Lakshmikantham V., and Leela S. Nonlinear Differential Equations in Abstract Spaces (1981), Pergamon Press, Oxford
11. Liu B. Positive solutions of a nonlinear four-point boundary value problems in Banach spaces. J. Math. Anal. Appl. 305 (2005) 253-276
12. Liu Y. Multiple positive solutions to fourth-order singular boundary value problems in abstract space. Electron. J. Differential Equation 2004 120 (2004) 1-13
13. Ma R. Existence theorems for a second order m-point boundary value problem. J. Math. Anal. Appl. 211 (1997) 545-555
14. Ma R. Existence of solutions of nonlinear m-point boundary value problem. J. Math. Anal. Appl. 256 (2001) 556-567
15. Potter A.J.B. A fixed point theorem for positive K-set contractions. Proc. Edinburgh Math. Soc. 19 (1974) 93-102
16. Webb T.R.L. Positive solutions of some three-point value problem via fixed point index theory. Nonlinear Anal. 47 (2001) 4319-4332