TRIPLE POSITIVE SOLUTIONS OF NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEMS

In this paper we consider the following nonlinear third order two-point boundary value problem \begin{align*} & x'''(t)+f(t,x(t))=0,\quad a \lt t \lt b,\\ & x(a)=x''(a)=x(b)=0. \end{align*} By using the Leggett-Williams and Krasnosel'skii fixed-point theorems, we offer criteria for the existence of three positive solutions to the boundary value problem. Examples are also included to illustrate the results obtained.