Multiple positive solutions of the singular boundary value problems for second-order differential equations on the half-line

In this paper, the existence of multiple positive solutions for singular Sturm–Liouville boundary value problems on the half-line is investigated. By applying the fixed point index theorem of cone map, some existence and multiplicity results of positive solutions are derived. Our results improve and generalize many well-known results. Two examples are presented to demonstrate the application of our main results.