Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

Document Type: Research articles


Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.


In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime prime }(0)=0, hspace{1cm} u^{prime prime }(1)- alpha u^{prime prime }(eta)=0, & end{array} right. end{eqnarray*} where $beta > 0, 0< eta 0$.