Exact interval of parameter and two infinite families of positive solutions for a nth order impulsive singular equation

In this article we establish the exactly determined open interval of positive parameter λ in which the nth order impulsive singular equation has two infinite families of positive solutions. Noticing that λ>0 and ck≠0(k=1,2,…,m), our main results improve and extend many recent results. Our approach is largely based on the theory of fixed point index, transformation technique and Hölder's inequality.