Abstract: By using fixed point index theory, we present the
existence of positive solutions to the singular boundary value problem and with where g, p
may be singular at and/or 1. The value of l is
chosen so that the boundary value problem has at least one or two positive
solutions. In addition, we derive an explicit interval for l such that for any l in
this interval, the existence of at least one positive solution to the boundary
value problem is guaranteed, and the existence of two positive solutions for l in an appropriate interval is also discussed. Our
results significantly extend and improve many known results even for
non-singular cases.
Keywords and phrases: singular differential equation, positive solutions, fixed point index, cone, BVP.
