Positive solutions for a class of 2n2nth-order singular boundary value problems

We establish sufficient and necessary conditions for guaranteeing the existence of C2n−2[0,1]C2n−2[0,1] as well as C2n−1[0,1]C2n−1[0,1] positive solutions for 2n2nth-order singular boundary value problems. The arguments are based upon the fixed point theorem an the maximal principle, as well as constructing lower and upper solutions. Our nonlinearity f(t,x1,x2,…,xn)f(t,x1,x2,…,xn) may be singular at xi=0,i=1,2,…,n,t=0xi=0,i=1,2,…,n,t=0 and/or t=1t=1. Meanwhile, an example is worked out to demonstrate the main results.