Positive solutions of higher-order singular boundary value problems

Some results of existence of positive solutions for singular boundary value problem $$left{begin{array}{l}displaystyle (-1)^{m}u^{(2m)}(t)=p(t)f(u(t)),quad tin(0,1),[2mm]displaystyle u^{(i)}(0)=u^{(i)}(1)=0,quad i=0,ldots,m-1,end{array}right.$$ are given, where the function p(t) may be singular at t=0,1. Our analysis relies on the variational method.