Positive solutions of nonlinear m-point boundary value problems on a measure chain

Journal of Difference Equations and Applications

Volumn 9, Issue 1, 2003, Pages 121-133

  Kong, Lingju ^a   Kong, Qingkai ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Existence; Fixed point index argument; M point boundary value problems; Positive solutions

Indexed keywords

EID: 0037241501     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/10236100309487539     Document Type: Article

References (24)

1. R.P. Agarwal and M. Bohner, Quadratic functions for second order matrix equations on time scales, Nonlinear Anal., 33 (1998), 675-692.
2. R. P. Agarwal and M. Bohner, Basic calculus on time scales and its applications, Results Math., 35 (1999), 3-22.
3. R. P. Agarwal, M. Bohner and P. Wong, Sturm-Liouville eigenvalue problems on time scales, Appl. Math. Comput., 99 (1999), 153-166.
4. C. Ahlbrandt, M. Bohner and J. Ridenhour, Hamiltonian systems on time scales, J. Math. Anal. Appl., 250 (2000), 561-578.
5. C. Ahlbrandt and A. Peterson, Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations, Kluwer, Boston, 1996.
6. B. Aulbach and S. Hilger, Linear Dynamic Processes with Inhomogeneous Time Scale Nonlinear Dynamics and Quantum Dynamical System, Math. Res., 59, Academic Verlag, Berlin, 1990.
7. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001.
8. C. J. Chyan and J. Henderson, Eigenvalue problems for nonlinear differential equations on a measure chain, J. Math. Anal. Appl., 245 (2000), 547-559.
9. C. J. Chyan, J. Henderson and H. C. Lo, Positive solutions in an annulus for nonlinear differential equations on a measure chain, Tamkang J. Math., 30 (1999), 231-240.
10. L. H. Erbe and S. Hilger, Sturmian theory on measure chains, Differ. Equs Dyn. Syst., 1 (1993), 223-246.
11. L. H. Erbe and A. Peterson, Green's function and comparison theorems for differential equations on measure chains, Dyn. Continuous, Discrete Impulsive Syst., 6 (1999), 121-137.
12. L. H. Erbe and A. Peterson, Positive solutions for a nonlinear differential equations on a measure chain, Math. Comput. Model., 32 (2000), 571-585.
13. W. Feng and J. R. L. Webb, Solvability of a three-point nonlinear boundary value problems at resonance, Nonlinear Anal., 30 (1997), 3227-3238.
14. W. Feng and J. R. L. Webb, Solvability of a m -point boundary value problems with nonlinear growth, J. Math. Anal. Appl., 212 (1997), 467-480.
15. W. Fang, On a m -point nonlinear boundary value problem, Nonlinear Anal., 30 (1997), 5369-5374.
16. D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Orlando, 1988.
17. C. P. Gupta, A generalized multi-point boundary value problem for second order ordinary differential equations, Appl. Math. Comput., 89 (1998), 133-146.
18. J. Henderson, Multiple solutions for 2 mth order Sturm-Liouville boundary value problems on a measure chain, J. Differ. Equs Appl., 6 (2000), 417-429.
19. S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Resultate Math., 18 (1990), 18-56.
20. V. A. Il'in and E. I. Moiseev, Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator, Differ. Eqs, 23 (1987), 979-987.
21. B. Kaymakçalan, V. Lakshmikantham and S. Sivasundaram, Dynamic Systems on Measure Chains Mathematics and its Applications, Vol. 370 Kluwer Academic, Dordrecht, 1996.
22. R.Y. Ma, Existence theorems for a second order m -point point value problem, J. Math. Anal. Appl., 211 (1997), 545-555.
23. [23] R. Y. Ma, Positive solutions of a nonlinear three-point boundary value problem, Electron. J. Differ. Eqs, 34 (1999), 1-8.
24. R. Y. Ma, Existence of solutions of nonlinear m-point boundary value problems, J. Math. Anal. Appl., 256 (2001), 556-567.