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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)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 679-686 More about this Journal
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
Fourth-order four-point Sturm-Liouville boundary value problem; positive solution; existence; cone; fixed point;
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