참고문헌
- R. P. Agarwal and D. O'Regan, Nonlinear boundary value problems on time scales, Nonlinear Anal. 44 (2001), no. 4, 527-535. https://doi.org/10.1016/S0362-546X(99)00290-4
- R. P. Agarwal, V. Otero-Espinar, K. Perera, and D. R. Vivero, Multiple positive solutions of singular Dirichlet problems on time scales via variational methods, Nonlinear Anal. 67 (2007), no. 2, 368-381. https://doi.org/10.1016/j.na.2006.05.014
- D. R. Anderson, Solutions to second-order three-point problems on time scales, J. Dif- ference Equ. Appl. 8 (2002), no. 8, 673-688. https://doi.org/10.1080/1023619021000000717
- D. R. Anderson, Existence of solutions for nonlinear multi-point problems on time scales, Dy- nam. Syst. Appl. 15 (2006), no. 1, 21-33.
- D. R. Anderson and R. Y. Ma, Second-order n-point eigenvalue problems on time scales, Adv. Difference Equ. 2006 (2006), Art. ID 59572, 17 pp.
- D. R. Anderson and P. J. Y. Wong, Positive solutions for second-order semipositone problems on time scales, Comput. Math. Appl. 58 (2009), no. 2, 281-291. https://doi.org/10.1016/j.camwa.2009.02.033
- D. R. Anderson and C. B. Zhai, Positive solutions to semi-positone second-order three- point problems on time scales, Appl. Math. Comput. 215 (2010), no. 10, 3713-3720. https://doi.org/10.1016/j.amc.2009.11.010
- F. M. Atici, D. C. Biles, and A. Lebedinsky, An application of time scales to economics, Math. Comput. Modelling 43 (2006), no. 7-8, 718-726. https://doi.org/10.1016/j.mcm.2005.08.014
- F. M. Atici and G. Sh. Guseinov, On Green's functions and positive solutions for bound- ary value problems on time scales, J. Comput. Appl. Math. 141 (2002), no. 1-2, 75-99. https://doi.org/10.1016/S0377-0427(01)00437-X
- M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
- M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
- J. J. Dacunha, J. M. Davis, and P. K. Singh, Existence results for singular three point boundary value problems on time scales, J. Math. Anal. Appl. 295 (2004), no. 2, 378- 391. https://doi.org/10.1016/j.jmaa.2004.02.049
- N. A. Hamal and F. Yoruk, Positive solutions of nonlinear m-point boundary value problems on time scales, J. Comput. Appl. Math. 231 (2009), no. 1, 92-105. https://doi.org/10.1016/j.cam.2009.02.003
- S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18 (1990), no. 1-2, 18-56. https://doi.org/10.1007/BF03323153
- V. Jamieson and V. Spedding, Taming nature's numbers, New Scientist: the global science and technology weekly 2404 (2003), 28-31.
- T. Jankowski, On dynamic equations with deviating arguments, Appl. Math. Comput. 208 (2009), no. 2, 423-426. https://doi.org/10.1016/j.amc.2008.12.011
- E. R. Kaufmann, Positive solutions of a three-point boundary value problem on a time scale, Electron. J. Differential Equations 2003 (2003), no. 82, 1-11.
- Z. Liang, Existence and uniqueness of fixed points for mixed monotone operators, Jour- nal of Dezhou University 24 (2008), no. 4, 1-6 (in Chinese).
- H. Luo, Positive solutions to singular multi-point dynamic eigenvalue problems with mixed derivatives, Nonlinear Anal. 70 (2009), no. 4, 1679-1691. https://doi.org/10.1016/j.na.2008.02.051
- Y. Sang, Successive iteration and positive solutions for nonlinear m-point boundary value problems on time scales, Discrete Dyn. Nat. Soc. 2009 (2009), Article ID 618413, 13 pages.
- Y. Sang, Z. Wei, and W. Dong, Existence and uniqueness of positive solutions for discrete fourth-order Lidstone problem with a parameter, Adv. Difference Equ. 2010 (2010), Article ID 971540, 18 pages.
- J. Sun, Existence of positive solution to second-order three-point BVPs on time scales, Bound. Value Probl. 2009 (2009), Article ID 685040, 6 pages.
- C. C. Tisdell and A. Zaidi, Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling, Nonlinear Anal. 68 (2008), no. 11, 3504-3524. https://doi.org/10.1016/j.na.2007.03.043
- P. Wang, H. Wu, and Y. Wu, Higher even-order convergence and coupled solutions for second-order boundary value problems on time scales, Comput. Math. Appl. 55 (2008), no. 8, 1693-1705. https://doi.org/10.1016/j.camwa.2007.06.026
-
C. Zhai and X. Cao, Fixed point theorems for
${\tau}-{\varphi}$ -concave operators and applications, Comput. Math. Appl. 59 (2010), no. 1, 532-538. https://doi.org/10.1016/j.camwa.2009.06.016 - X. Zhao and W. Ge, Multiple positive solutions for time scale boundary value problems on infinite intervals, Acta. Appl. Math. 106 (2009), no. 2, 265-273. https://doi.org/10.1007/s10440-008-9294-3