




Volume 34 • Number 3 • 2011 

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A New Comparison Theorem and the Solvability of a ThirdOrder TwoPoint Boundary Value Problem
Yuqiang Feng and Guangjun Qu
Abstract.
A new comparison theorem is proved and then used to investigate the solvability of a thirdorder twopoint 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.
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