Volume 34 • Number 3 • 2011   • A New Comparison Theorem and the Solvability of a Third-Order Two-Point Boundary Value Problem Yuqiang Feng and Guangjun Qu Abstract. A new comparison theorem is proved and then used to investigate the solvability of a third-order two-point boundary value problem \begin{equation*} \left \{\begin{array}{lll} u'''(t)+f(t,u(t),u'(t),u''(t))=0, \\u(0)=u'(2\pi)=0,\\ u''(0)=u''(2\pi). \end{array} \right. \end{equation*} Some existence results are established for this problem via upper and lower solutions method and fixed point theory. 2010 Mathematics Subject Classification: 34B15, 34C05. Full text: PDF