Positive solutions to a new kind Sturm-Liouville-like four-point boundary value problem

In this paper, we considered the following four-point boundary value problem y Elsevi tion of Enginee J. Zhao) x00ðtÞ þ hðtÞf ðt; xðtÞ; x0ðtÞÞ 1⁄4 0; 0 < t < 1; x0ð0Þ a1xðnÞ 1⁄4 0; x0ð1Þ þ a2xðgÞ 1⁄4 0; where 0 < a1 < n ; 0 < a2 < 1 1 g ; 0 < n < g < 1; a1a2g a1a2n þ a1 þ a2 > 0: By applying fixed-point theorems, we obtain a variety of existence results. In particular, our four-point boundary condition is a new kind Sturm–Liouville-like boundary condition, which has rarely been considered up to now. 2010 Published by Elsevier Inc.