A NEW THEOREM OF EXISTENCE TO FOURTH-ORDER BOUNDARY VALUE PROBLEM

Abstract

A new theorem of existence for fourth-order boundary value problem\begin{eqnarray*}\Delta ^4x(t-2) &=&a(t)f(x(t)),\quad t\in [2,T], \\x(0) &=&x(T+2)=0, \\\Delta ^2x(0) &=&\Delta ^2x(T)=0\end{eqnarray*}is obtained by using a Fixed Point Theorem.