**REFERENCES**

[1] P. Agasti and P. K. Kundu, Incoming waves against a vertical cliff in two liquids, Adv. Appl.

Fluid Mech. 7 (2010), no. 1, 71–80.

[2] P. Bailey, L. Shampine and P. Waltman, Nonlinear Two Point Boundary Value Problems, Academic Press, New York, 1968.

[3] D. Barr and T. Sherman, Existence and uniqueness of solutions of three-point boundary value

problems, J. Differential Equations 13 (1973), 197–212.

[4] D. Barr and P. Miletta, An existence and uniqueness criterion for solutions of boundary value

problems, J. Differential Equations 16 (1974), 460–471.

[5] D. Barr and P. Miletta, A necessary and sufficient condition for uniqueness of solutions to two

point boundary value problems, Pacific J. Math. 57 (1975), 325–330.

[6] M. Eggensperger, E. R. Kaufmann and N. Kosmatov, Solution matching for a three-point

boundary-value problem on a time scale, Electron. J. Diff. Equ. 2004 (2004), no. 91, 1–7.

[7] J. Henderson, Three-point boundary value problems for ordinary differential equations by

matching solutions, Nonlinear Anal. 7 (1983), 411–417.

[8] J. Henderson, Boundary value problems for third order differential equations by solution

matching, Electron. J. Qual. Theory Differ. Equ., Spec. Ed. I, (2009), 1–9.

[9] J. Henderson, J. Ehrke and C. Kunkel, Five-point boundary value problems for n-th order

differential equations by solution matching, Involve 1 (2008), 1–7.

[10] J. Henderson and X. Liu, BVPs with odd differences of gaps in boundary conditions for nth

order ODE’s by matching solutions, Computers & Mathematics with Applications 62 (2011), 3722–3728.

[11] J. Henderson and K. R. Prasad, Existence and uniqueness of solutions of three-point boundary

value problems on time scales by solution matching, Nonlinear Stud. 8 (2001), 1–12.

[12] J. Henderson and R. D. Taunton, Solutions of boundary value problems by matching methods,

Appl. Anal. 49 (1993), 235–246.

[13] R. D. Taunton, Boundary Value Problems by Matching and Functional Differential Equations,

PhD dissertation, Auburn University, 1995.

[14] J. Henderson and C. C. Tisdell, Five-point boundary value problems for third-order differential

equations by solution matching, Math. Comput. Modelling 42 (2005), 133–137.

[15] V. Lakshmikantham and K. N. Murty, Theory of differential inequalities and three-point

boundary value problems, Panamer. Math. J. 1 (1991), 1–9.

[16] X. Y. Liu, Nonlocal boundary value problems for nth order ordinary differential equations by

matching solutions, Electron. J. Diff. Equ. 2011 (2011), pp. 1-9.

[17] X. Y. Liu, Nonlocal boundary value problems with even gaps in boundary conditions for third

order differential equations, Dynam. Systems Appl., 23 (2014), 465–478.

[18] X. Y. Liu, Boundary value problems with gaps in boundary conditions for differential equations

by matching solutions, Comm. Appl. Nonlinear Anal. 17 (2010), 81–88.

[19] V. R. G. Moorti and J. B. Garner, Existence-uniqueness theorems for three-point boundary

value problems for nth-order nonlinear differential equations, J. Differential Equations 29 (1978), 205–213.

[20] K. N. Murty, Three point boundary value problems, existence and uniqueness, J. Math. Phys.

Sci. 11 (1977), 265–272.

[21] K. N. Murty and Y. S. Rao, A theory for existence and uniqueness of solutions to three point

boundary value problems, J. Math. Anal. Appl. 167 (1992), 43–48.

[22] M. S. N. Murty and G. Suresh Kumar, Extension Of Liapunov Theory To Five-Point Boundary

Value Problems For Third Order Differential Equations, Novi Sad J. Math. 37 (2007), 85–92.

[23] K. N. Murty and G. V. R. L. Sarma, Theory of differential inequalities for two-point boundary

value problems and their applications to three-point B.V.Ps associated with nth order nonlinear

system of differential equations, Appl. Anal. 81 (2002), 39–49.

[24] M. F. Natale, E. A. Santillan Marcus and D. A. Tarzia, Explicit solutions for one-dimensional

two-phase free boundary problems with either shrinkage or expansion, Nonlinear Anal. Real

World Appl. 11 (2010), no. 3, 1946–1952.

[25] M. H. Pei and S. K. Chang, Existence and uniqueness of solutions of two-point and three-point

boundary value problems for nth-order nonlinear differential equations, Kyungpook Math. J.

41 (2001), no. 2, 289–298.

[26] M. H. Pei and S. K. Chang, Nonlinear three-point boundary value problems for nth-order

nonlinear differential equations, Acta Math. Sinica (Chin. Ser.) 48 (2005), 763–772.

[27] D. R. K. S. Rao, K. N. Murty and A. S. Rao, On three-point boundary value problems

associated with third order differential equations, Nonlinear Anal. 5 (1981), 669–673.

[28] E. Rohan and V. Lukeˇs, Homogenization of the acoustic transmission through a perforated

layer, J. Comput. Appl. Math. 234 (2010), no. 6, 1876–1885.

[29] Y. L. Shi and M. H. Pei, Two-point and three-point boundary value problems for nth-order

nonlinear differential equations, Appl. Anal. 85 (2006), no. 12, 1421–1432.

[30] T. Yoshizawa, Stability Theory by Liapunov’s Second Method, Publ. Math. Soc. Japan, no. 9,

Math. Soc. Japan, Tokyo, 1966.

[31] Y. Zhang, Q. Zou and D. Greaves, Numerical simulation of free-surface flow using the level-set

method with global mass correction, Internat. J. Numer. Methods Fluids 63 (2010), no. 6,

651–680.