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

Abstract

In this article we establish the exactly determined open interval of positive parameter λ in which the n t h order impulsive singular equation has two infinite families of positive solutions. Noticing that λ > 0 and c k ≠ 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.