**REFERENCES**

[1] J. M. Davis and J. Henderson, Uniqueness implies existence for fourth-order Lidstone boundary

value problems, Panamer. Math. J. 8 (1998), no. 4, 23–35.

[2] W. Feng and J. Zhang, Existence of positive solution for fourth order superlinear singular

semipositone differential system, Pure and Appl. Math. J. 2 (2013), 179-183.

[3] J. R. Graef, J. Henderson, and B. Yang, Positive solutions to a fourth order three point boundary

value problem, Discrete Contin. Dyn. Syst. 2009 (2009), Dynamical Systems, Differential

Equations and Applications, 7th AIMS Conference, suppl., 269–275.

[4] C. P. Gupta, Existence and uniqueness results for bending of an elastic beam at resonance, J.

Math. Anal. Appl. 135 (1988), no. 1, 208-225.

[5] J. Henderson and R. W. McGwier, Jr., Uniqueness, existence, and optimality for fourth-order

Lipschitz equations, J. Differential Equations 67 (1987), no. 3, 414–440.

[6] M. A. Krasnosel’ski˘ı, Topological Methods in the Theory of Nonlinear Integral Equations,

MacMillan, New York, 1964.

[7] W. Li, Y. Fei, B. Shan, and Y. Pang, Positive solutions of a singular semipositone boundary

value problems for fourth-order coupled difference equations, Adv. Difference Equ. 2012 (2012), 11 pp.

[8] R. Ma, Multiple positive solutions for a semipositone fourth-order boundary value problem,

Hiroshima Math. J. 33 (2013), 217-227.

[9] Y. Sun, Existence of positive solutions for fourth-order semipositone multi-point boundary

value problems with a sign-changing nonlinear term, Bound. Value Prob. 2012 (2012), 16 pp.

[10] S. Timoshenko and J. M. Gere, Mechanics of Materials, Van Nostrand Reinhold Co., New York, 1972.

[11] J. R. L. Webb and M. Zima, Multiple positive solutions of resonant and non-resonant non-local

fourth-order boundary value problems, Glasg. Math. J. 54 (2012), no. 1, 225–240.

[12] F. Zhu, L. Liu, and Y. Wu, Positive solutions for systems of a nonlinear fourth-order singular

semipositone boundary value problems, Appl. Math. Comput. 216 (2010), no. 2, 448-457.