Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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POSITIVE SOLUTION FOR FOURTH-ORDER FOUR-POINT STURM-LIOUVILLE BOUNDARY VALUE PROBLEM

  • Sun, Jian-Ping (Department of Applied Mathematics, Lanzhou University of Technology) ;
  • Wang, Xiao-Yun (Department of Applied Mathematics, Lanzhou University of Technology)
  • Received : 2009.10.23
  • Accepted : 2009.11.30
  • Published : 2010.05.30
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Abstract

This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,\;u(t),\;u^{\prime\prime}(t))$, $0\;{\leq}\;t\;{\leq}1$, ${\alpha}u(0)-{\beta}u^{\prime}(0)={\gamma}u(1)+{\delta}u^{\prime}(1)=0$, $au^{\prime\prime}(\xi_1)-bu^{\prime\prime\prime}(\xi_1)=cu^{\prime\prime}(\xi_2)+du^{\prime\prime\prime}(\xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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