# Journal of Advances in Applied Mathematics

### Positive Solutions of Some Fourth-order Two Point Boundary Value Problem with All Order Derivatives

Download PDF (552 KB) PP. 15 - 22 Pub. Date: January 1, 2017

### Author(s)

**Fei Yang**^{*}

Nanchang Institute of Science and Technology, Nanchang 330108, Jiangxi, P. R. China**Yuanjian Lin**

Nanchang Institute of Science and Technology, Nanchang 330108, Jiangxi, P. R. China

### Abstract

### Keywords

### References

[1] Z.B. Bai, The method of lower and upper solution for a bending of an elastic beam equation, J. Math. Anal. Appl. 248 (2000) 195-202.

[2] R. Ma, J. ZHANG, S. Fu. The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems. J. Math. Anal. Appl. 1997, 215: 415-422.

[3] A. B. LIU. Positive Solutions of Fourth-Order Two-Point Boundary Value Problems. Appl. Math. Comput. 2004, 148: 407-420.

[4] Z.B. BAI, H.Y. Wang. On the Positive Solutions of Some Nonlinear Fourth-Order Beam Equations. J. Math. Anal. Appl. 2002, 270: 357-368.

[5] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New york, 1988.

[6] Q.L. Yao, Local existence of multiple positive solutions to a singular cantilever beam equation, J. Math. Anal. Appl. 363 (2010) 138-154.

[7] F. LI, Q. ZHANG, Z. LIANG. Existence and Multiplicity of Solutions of a Kind of Fourth-Order Boundary Value Problem. Nonlinear Anal, 2005, 62: 803-816.

[8] Y.X. Li, Positive solutions of fourth-order boundary value problems with two parameters, J. Math. Anal. Appl. 281 (2003) 477-484.

[9] X.Z Lv, L.B Wang, M.H Pei, Monotone positive solution of a fourth-order BVP with integral boundary conditionscnBoundary Value Problems (2015) 2015:172,1-12.

[10] Yanping Guo, Positive solutions for three-point boundary value problems with dependence on the first order derivatives, Journal of Mathematical Analysis and Applications 290 (2004) 291-301.

[11] Y.P Guo, F Yang, Y.C Liang, Positive solutions for nonlocal fourth-order boundary value problems with allorder derivatives, Boundary Value Problems (2012) 2012:29, 1-21.