Triple positive solutions of nonlinear third order boundary value problems (Q842019)

The authors study the following nonlinear third order two--point boundary value problem \[ \begin{cases} x'''(t)=f(t,x(t))=0, \;a<t<b,\\ x(a)=x''(a)=x(b)=0. \end{cases}\tag{*} \] By using Leggett-Williams and Krasnosel'skii's fixed-point theorems, the authors obtain some criteria for the existence of three positive solutions to (*). Three examples are given to illustrate the main results.