摘要
The singular boundary value problem{φ^（4）（x）-h（x）f（φ（x））=0,0〈x〈1, φ（0）=φ（1）=φ′（0）=φ′（1）=0.is considered under some conditions concerning the first eigenvaiues corresponding to the relevant linear operators, where h（x） is allowed to be singular at both x = 0 and x = 1. The existence results of positive solutions are obtained by means of the cone theory and the fixed point index.
The singular boundary value problem (4)(x) h(x)f((x)) = 0, 0 < x < 1, (0) = (1) = (0) = (1) = 0 is considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where h(x) is allowed to be singular at both x = 0 and x = 1. The existence results of positive solutions are obtained by means of the cone theory and the fixed point index.
基金
the National Natural Science Foundation of China （No. 10671167）
the Chunlei Program of SDUST （No. 2008AZZ044）.
