Find in Library

<p>Abstract</p> <p>We establish existence results of the following three-point boundary value problems: <inline-formula> <graphic file="1687-2770-2011-901796-i1.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-901796-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-901796-i3.gif"/></inline-formula> and <inline-formula> <graphic file="1687-2770-2011-901796-i4.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2011-901796-i5.gif"/></inline-formula> and <inline-formula> <graphic file="1687-2770-2011-901796-i6.gif"/></inline-formula>. The approach applied in this paper is upper and lower solution method associated with basic degree theory or Schauder's fixed point theorem. We deal with this problem with the function <inline-formula> <graphic file="1687-2770-2011-901796-i7.gif"/></inline-formula> which is Carath&#233;odory or singular on its domain.</p>