Existence of positive solution for second-order nonlinear impulsive singular differential equations of mixed type in Banach spaces

In this paper, by constructing a closed convex set and using the fixed point theory of completely continuous operators, we investigate the existence of positive solutions for an initial value problem of second-order nonlinear impulsive singular integro-differential equations in a Banach space. The method used in this paper is different from that in the literature.