Existence of Multiple Positive Solutions for nth Order Two-Point Boundary Value Problems on Time Scales

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References

[1] G. H. Meyer, “Initial Value Methods for Boundary Value Problems,” Journal of Applied Mathematics and Computing, Vol. 158, No. 1, 2004, pp. 345-351.

[2] J. P. Keener, “Principles of Applied Mathematics,” Addison-Wesley, Redwood City, 1988.

[3] P. C. Wayner, Y. K. Kao and L. V. Lacroin, “The Interlimne Heat Transfer Coefficient of an Eveporating Wetting Film,” International Journal of Heat and Mass Transfer, Vol. 19, No. 5, 1976, pp. 487-492.
doi:10.1016/0017-9310(76)90161-7

[4] M. Bohner and A. C. Peterson, “Dynamic Equations on Time Scales, an Introduction with Applications,” Birkhauser, Boston, 2001.

[5] L. H. Erbe and H. Wang, “On the Existence of Positive Solutions of Ordinary Differential Equations,” Proceedings of the American Mathematical Society, Vol. 120, No. 3, 1994, pp. 743-748.
doi:10.1090/S0002-9939-1994-1204373-9

[6] P. W. Eloe and J. Henderson, “Positive Solutions for (n-1,1) Conjugate Boundary Value Problems,” Nonlinear Analysis, Vol. 28, No. 10, 1997, pp. 1669-1680.
doi:10.1016/0362-546X(95)00238-Q

[7] P. W. Eloe and J. Henderson, “Positive Solutions and Nonlinear (k,n-k) Conjugate Eigenvalue Problems,” Journal of Differential Equations Dynamical Systems, Vol. 6, 1998, pp. 309-317.

[8] F. M. Atici and G. Sh. Guseinov, “Positive Periodic Solutions for Nonlinear Difference Equations with Periodic Coefficients,” Journal of Mathematical Analysis and Applications, Vol. 232, No. 1, 1999, pp. 166-182.
doi:10.1006/jmaa.1998.6257

[9] D. R. Anderson and R. I. Avery, “Multiple Positive Solutions to a Third-Order Discrete Focal Boundary Value Problem,” Journal of Computers and Mathematics with Applications, Vol. 42, No. 3-5, 2001, pp. 333-340.
doi:10.1016/S0898-1221(01)00158-4

[10] R. I. Avery and A. C. Peterson, “Multiple Positive Solutions of a Discrete Second Order Conjugate Problem,” Panamerican Mathematical Journal, Vol. 8, No. 3, 1998, pp. 1-12.

[11] R. P. Agarwal, D. O’Regan and P. J. Y. Wong, “Positive Solutions of Differential, Difference and Integral Equations,” Kluwer Academic Publishers, Dordrecht, 1999.

[12] K. Deimling, “Nonlinear Functional Analysis,” Springer, New York, 1985. doi:10.1007/978-3-662-00547-7

[13] M. Gregus, “Third Order Linear Differential Equations and Mathematical Applications,” Reidel, Dordrecht, 1987.
doi:10.1007/978-94-009-3715-4

[14] D. Guo and V. Lakshmikantham, “Nonlinear Problems in Abstract Cones,” Acadamic Press, San Diego, 1988.

[15] J. Henderson and S. K. Ntouyas, “Positive Solutions for System of nth Order Three-Point Nonlocal Boundary Value Problems,” Electronic Journal of Qualitative Theory of Differential Equations, Vol. 18, No. 5, 2007, pp. 1-12.

[16] B. Hopkins and N. Kosmator, “Third Order Boundary Value Problem with Sign-Changing Solution,” Nonlinear Analysis, Vol. 67, No. 1, 2007, pp. 126-137.
doi:10.1016/j.na.2006.05.003

[17] S. Li, “Positive Solutions of Nonlinear Singular Third Order Two-Point Boundary Value Problem,” Journal of Mathematical Analysis and Applications, Vol. 323, No. 1, 2006, pp. 413-425. doi:10.1016/j.jmaa.2005.10.037

[18] M. El-Shehed, “Positive Solutions of Boundary Value Problems for n^{th} Order Differential Equations,” Electronic Journal of Qualitative Theory of Differential Equations, No. 1, 2008, pp. 1-9.

[19] K. R. Prasad and P. Murali, “Eigenvalue Intervals for nth Order Differential Equations on Time Scales,” International Journal of Pure and Applied Mathematics, Vol. 44, No. 5, 2008, pp. 737-753.

[20] R. W. Leggett and L. R. Williams, “Multiple Positive Fixed Points of Nonlinear Operator on Order Banach Spaces,” Indiana University Mathematics Journal, Vol. 28, No. 4, 1979, pp. 673-688. doi:10.1512/iumj.1979.28.28046