# POSITIVE SOLUTIONS OF FOURTH-ORDER BOUNDARY VALUE PROBLEM WITH VARIABLE PARAMETERS

Volume 1, Issue 1, pp 21-30
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### Authors

XIN DONG - College of Information Science and Engineering,Shandong University of Science and Technology, Qing Dao, 266510, P. R. China.. ZHANBING BAI - College of Information Science and Engineering,Shandong University of Science and Technology, Qing Dao, 266510, P. R. China..

### Abstract

By means of calculation of the fixed point index in cone we consider the existence of one or two positive solutions for the fourth-order boundary value problem with variable parameters $\begin{cases} u^{(4)}(t) + B(t)u''(t) - A(t)u(t) = f(t, u(t), u''(t)),\,\,\,\,\, 0 < t < 1,\\ u(0) = u(1) = u''(0) = u''(1) = 0, \end{cases}$ where $A(t),B(t) \in C[0, 1]$ and $f(t, u, v) : [0, 1]\times [0,\infty)\times R \rightarrow [0,\infty)$ is continuous.

### Share and Cite

##### ISRP Style

XIN DONG, ZHANBING BAI, POSITIVE SOLUTIONS OF FOURTH-ORDER BOUNDARY VALUE PROBLEM WITH VARIABLE PARAMETERS, Journal of Nonlinear Sciences and Applications, 1 (2008), no. 1, 21-30

##### AMA Style

DONG XIN, BAI ZHANBING, POSITIVE SOLUTIONS OF FOURTH-ORDER BOUNDARY VALUE PROBLEM WITH VARIABLE PARAMETERS. J. Nonlinear Sci. Appl. (2008); 1(1):21-30

##### Chicago/Turabian Style

DONG , XIN, BAI, ZHANBING. "POSITIVE SOLUTIONS OF FOURTH-ORDER BOUNDARY VALUE PROBLEM WITH VARIABLE PARAMETERS." Journal of Nonlinear Sciences and Applications, 1, no. 1 (2008): 21-30

### Keywords

• Boundary value problem
• positive solution
• fixed point
• cone.

•  34B15
•  34B18

### References

• [1] R. P. Agarwal , On fourth-order boundary value problems arising in beam analysis, Diff. Inte. Eqns. , 2 (1989), 91–110

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

• [3] Z. B. Bai, Positive solutions for some second-order four-point boundary value problems, J. Math. Anal. Appl., 2 330 (2007), 34–50

• [4] Z. B. Bai, The method of lower and upper solutions for some fourth-order boundary value problems, Nonlinear Anal. , 67 (2007), 1704–1709

• [5] G. Q. Chai, Existence of positive solutions for fourth-order boundary value problem with variable parameters, Nonlinear Anal. , 66 (2007), 870–880

• [6] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New york (1988)

• [7] Y. X. Li , Existence and method of lower and upper solutions for fourth-order nonlinear boundary value problems, Acta Mathmatic Scientia , 23 (2003), 245–252

• [8] Y. X. Li, Existence and multiplicity of positive solutions for fourth-order boundary value problems, Acta Mathematicae Applicatae Sinica, 26 (2003), 109–116

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

• [10] R. Y. Ma, H. Y. Wang, Positive solutions of nonlinear three-point boundary-value problems, Nonlinear Anal., 279 (2003), 216–227

• [11] Z. L. Wei, C. C. Pang , Positive solutions and multiplicity of fourth-order m-point boundary value problem with two parameters, Nonlinear Anal., 67 (2007), 1586–1598