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

Volume 1, Issue 1, pp 21-30 http://dx.doi.org/10.22436/jnsa.001.01.04

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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.

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Keywords

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

MSC

•  34B15
•  34B18

References

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


• [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
  • View Article
  • MathSciNet
  • Google Scholar


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


• [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
  • View Article
  • Google Scholar


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


• [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
  • MathSciNet
  • Google Scholar


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


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


• [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
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH