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)=f(t,x(t),−x″(t)),t∈(0,1),x(0)=x(1)=x″(0)=x″(1)=0, where f(t,x,y)f(t,x,y) may be singular at t=0,1t=0,1; x=0x=0 and y=0y=0.