Existence Solution for 5th Order Differential Equations under Some Conditions

Sayada Nabhan Odda

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DOI: 10.4236/am.2010.14035                

Abstract

We study a nonlinear differential equations in the Banach space of real functions and continuous on a bounded and closed interval. With the help of a suitable theorems (fixed point) and some boundary conditions, the 5th order nonlinear differential equations has at least one positive solution.

Keywords

Fixed-Point Theorem, Banach Space, Nonlinear 5th Order Differential Equations

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. P. Agarwal and D. Oregan, “Global Existence for Nonlinear Operator Inclusion,” Computers & Mathematics with Applications, Vol. 38, No. 11-12, 1999, pp. 131 -139.
[2]	R. P. Agarwal, D. Oregan and P. J. Y. Wong, “Positive Solutions of Differential, Difference and Integral Equations,” Kluwer Academic, Dordrecht, 1999.
[3]	M. El-Shahed, “Positive Solutions for Nonlinear Singular Third Order Boundary Value Problem,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 2, 2009, pp. 424-429.
[4]	D. Guo and V. Lakshmikantham, “Nonlinear Problems in Abstract Cones,” Academic Press, San Diego, 1988.
[5]	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.
[6]	H. Sun and W. Wen, “On the Number of Positive Solutions for a Nonlinear Third Order Boundary Value Problem,” International Journal of Difference Equations, Vol. 1, No. 1, 2006, pp. 165- 176.
[7]	R. P. Agarwal, M. Meehan and D. Oregan, “Fixed Point and Applications,” Cambridge University Press, Cambridge, 2001.
[8]	B. Yang, “Positive Solutions for a Fourth Order Boundary Value Problem,” Electronic Journal of Qualitative Theory of differential Equations, Vol. 3, No. 1, 2005, pp. 1-17.
[9]	S. Q. Zhang, “Existence of Solution for a Boundary Value Problem of Fractional Order,” Acta Mathematica Scientica, Vol. 26, No. 2, 2006, pp. 220-228.