Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 143, pp. 1-8.

Title: Twin positive solutions for fourth-order two-point 
       boundary-value problems with sign changing nonlinearities

Authors: Yu Tian (Beijing Institute of Technology, China)
         Weigao Ge (Beijing Institute of Technology, China)

Abstract: 
 A new fixed point theorem on double cones is applied to obtain
 the existence of at least two positive solutions to
 \begin{gather*}
 (\Phi_p(y''(t))''-a(t)f(t,y(t),y''(t))=0,\quad 0<t<1,\\
 y(0)=y(1)=0=y''(0)=y''(1),
 \end{gather*}
 where $f:[0,1]\times[0,\infty)\times(-\infty,0]\to R,
 a\in L^1([0,1],(0,\infty)) $. We also give some examples to
 illustrate our results.

Submitted August 28, 2004. Published December 3, 2004.
Math Subject Classifications: 34B10, 34B15.
Key Words: Fourth-order two-point boundary-value problem; fixed
point theorem; double cones; positive solution.