University of MazandaranCaspian Journal of Mathematical Sciences (CJMS)1735-06111120120201Existence of positive solutions for fourth-order boundary value
problems with three- point boundary conditions3ENN. NYAMORADIDepartment of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah,
Iran.Journal Article20111126<p>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 $beta > 0, 0< eta 0$.</p>http://cjms.journals.umz.ac.ir/article_3_459da43ddb149ea17d0587b414c834f5.pdf