Existence and uniqueness theorems for fourth-order singular boundary value problems

By constructing a special cone and using cone compression and expansion fixed point theorem, the existence and uniqueness are established for the following singular fourth- order boundary value problems: x.4/.t/ D f .t; x.t/;􀀀x00.t//; t 2 .0; 1/; x.0/ D x.1/ D x00.0/ D x00.1/ D 0; where f .t; x; y/ may be singular at t D 0; 1; x D 0 and y D 0.