Positive solution for a class of nonlinear fourth-order boundary value problem

Abstract

<abstract><p>In this paper, we are concerned with the existence of positive solutions for boundary value problems of nonlinear fourth-order differential equations</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} &amp;&amp;u^{(4)}+c(x)u = \lambda a(x)f(u), \; \; x\in (0,1),\\ &amp;&amp;u(0) = u(1) = u''(0) = u''(1) = 0, \end{eqnarray*} $\end{document} </tex-math></disp-formula></p> <p>where $ a(x) $ may change signs. The proof of main results is based on Leray-Schauder's fixed point theorem and the properties of Green's function of the fourth-order differential operator $ L_cu = u^{(4)}+c(x)u $.</p></abstract>