Existence of positive solutions for singular boundary value problem on time scales

Journal of Mathematical Analysis and Applications

Volumn 325, Issue 1, 2007, Pages 517-528

  Hao, Zhao Cai ^a,b   Xiao, Ti Jun ^a   Liang, Jin ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b QUFU NORMAL UNIVERSITY   (China)

Author keywords

Boundary value problem; Positive solutions; Singular; Time scales

Indexed keywords

EID: 33750297329     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.01.083     Document Type: Article

References (22)

1. Akin E. Cauchy functions for dynamic equation on a measure chain. J. Math. Anal. Appl. 267 (2002) 97-115
2. Anderson D.R. Eigenvalue intervals for a two-point boundary value problem on a measure chain. J. Comput. Appl. Math. 141 (2002) 57-64
3. Aulbach B., and Hilger S. Linear dynamic processes with inhomogeneous time scale. Nonlinear Dynamics and Quantum Dynamical Systems. Math. Res. vol. 59 (1990), Akademie Verlag, Berlin 9-20
4. Bohner M., and Guseinov G.Sh. Improper integrals on time scales. Dynam. Syst. Appl. 12 (2003) 45-65
5. In: Bohner M., and Peterson A. (Eds). Advances in Dynamic Equations on Time Scales (2003), Birkhäuser, Boston
6. Chyan C.J., and Henderson J. Eigenvalue problem for nonlinear differential equations on a measure chain. J. Math. Anal. Appl. 245 (2000) 547-559
7. DaCunha J.J., Davis J.M., and Singh P.K. Existence results for singular three point boundary value problem on time scales. J. Math. Anal. Appl. 295 (2004) 378-391
8. Davis J.M., Henderson J., Prasad K.R., and Yin W. Eigenvalue intervals for nonlinear right focal problems. Appl. Anal. 74 (2000) 215-231
9. Eloe P.W., and Henderson J. Positive solutions and nonlinear (k, n - k) conjugate eigenvalue problems. Differential Equations Dynam. Systems 6 (1998) 309-317
10. Erbe L.H., and Hilger S. Sturmian theory on measure chains. Differential Equations Dynam. Systems 1 (1993) 223-244
11. Erbe L.H., and Peterson A. Green's functions and comparison theorems for differential equation on measure chains. Dyn. Contin. Discrete Impuls. Syst. 6 (1999) 121-137
12. Erbe L.H., and Peterson A. Eigenvalue conditions and positive solutions. J. Difference Equ. Appl. 6 (2000) 165-191
13. Erbe L.H., and Peterson A. Positive solutions for nonlinear differential equation on a measure chain. Math. Comput. Modelling 32 (2000) 571-585
14. Erbe L.H., and Wang H.Y. On the existence of positive solutions of ordinary difference equations. Proc. Amer. Math. Soc. 120 (1994) 743-748
15. Henderson J., and Wang H.Y. Positive solutions for nonlinear eigenvalue problems. J. Math. Anal. Appl. 208 (1997) 252-259
16. Hilger S. Analysis on measure chains-a unified approach to continuous and discrete calculus. Results Math. 18 (1990) 18-56
17. Hilger S. Differential and difference calculus-unified. Nonlinear Anal. 30 (1997) 2683-2694
18. Hong C.H., and Yeh C.C. Positive solutions for eigenvalue problems on a measure chain. Nonlinear Anal. 51 (2002) 499-507
19. Krasnosel'skii M.A. Positive Solutions of Operator Equations (1964), Noordhoff, Groningen
20. Lakshmikantham V., Sivasundaram S., and Kaymakcalan B. Dynamical Systems on Measure Chains (1996), Kluwer Academic, Boston
21. Lian W.C., Wong W.F., and Yeh C.C. On the existence of positive solutions of nonlinear differential equations. Proc. Amer. Math. Soc. 124 (1996) 1117-1126
22. Liang J., Xiao T.J., and Hao Z.C. Positive solutions of singular differential equations on measure chains. Comput. Math. Appl. 49 (2005) 651-663