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Triple positive solutions of three-point boundary value problems for fourth-order differential equations

Published: 01 September 2008 Publication History

Abstract

Using the Avery and Peterson fixed point theorem, we investigate the existence of three positive solutions for the fourth order three-point boundary value problem u^(^4^)(t)=h(t)f(t,u(t),u^''(t)),0 0, 0<@x<1 and h(t) is sign-changing on [0,1]. The interesting point is that the nonlinear term is allowed to depend on u^''.

References

[1]
Avery, R. and Henderson, J., Three positive fixed points of nonlinear operators on order Banach spaces. Comput. Math. Appl. v42. 313-322.
[2]
Bai, Z., Wang, Y. and Ge, W., Triple positive solutions for a class of two-point boundary-value problems. Electron. J. Differential Equations. 1-8.
[3]
Shu, X., Huang, L. and Li, Y., Triple positive solutions for a class of boundary value problems for second-order neutral functional differential equations. Nonlinear Anal. v65. 825-840.
[4]
Agarwal, R.P., Focal Boundary Value Problems for Differential and Difference Equations. 1998. Kluwer Academic, Dordrecht.
[5]
Bai, Z. and Wang, H., On positive solutions of some nonlinear fourth-order beam equations. J. Math. Anal. Appl. v270. 357-368.
[6]
Hao, Z., Liu, L. and Debnath, L., A necessary and sufficient condition for the existence of positive solutions of fourth-order singular boundary value problems. Appl. Math. Lett. v16. 279-285.
[7]
Li, F., Zhang, Q. and Liang, Z., Existence and multiplicity of solutions of a kind of fourth-order boundary value problem. Nonlinear Anal. v62. 803-816.
[8]
Li, Y., Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl. v281. 477-484.
[9]
Liu, B., Positive solutions of fourth-order two point boundary value problems. Appl. Math. Comput. v148. 407-420.
[10]
Liu, B., Positive solutions of three-point boundary value problems for the one-dimensional p-Laplacian with infinitely many singularities. Appl. Math. Lett. v17. 655-661.
[11]
Yang, D., Zhu, H. and Bai, C., Positive solutions for semipositone fourth-order two-point boundary value problems. Electron. J. Differential Equations. v16. 1-8.
[12]
Zhang, X., Liu, L. and Zou, H., Positive solutions of fourth-order singular three point eigenvalue problems. Appl. Math. Comput. v189. 1359-1367.
[13]
Zhang, M. and Wei, Z., Existence of positive solutions for fourth-order m-point boundary value problem with variable parameters. Appl. Math. Comput. v190. 1417-1431.

Cited By

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  • (2010)Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating ArgumentsJournal of Optimization Theory and Applications10.1007/s10957-010-9658-5146:1(105-115)Online publication date: 1-Jul-2010

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Published In

cover image Computers &amp; Mathematics with Applications
Computers & Mathematics with Applications  Volume 56, Issue 5
September, 2008
309 pages

Publisher

Pergamon Press, Inc.

United States

Publication History

Published: 01 September 2008

Author Tags

  1. Cone
  2. Fixed point theorem
  3. Positive solution
  4. Sign-changing
  5. Three-point boundary value problem

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Cited By

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  • (2010)Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating ArgumentsJournal of Optimization Theory and Applications10.1007/s10957-010-9658-5146:1(105-115)Online publication date: 1-Jul-2010

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