Positive Solutions of Singular Boundary Value Problems of Fourth-Order Differential Equations

摘要

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.