POSITIVE SOLUTIONS TO A TWO POINT SINGULAR BOUNDARY VALUE PROBLEM

We employ fixed point index theory to establish existence results for positive solutions to the singular boundary value problem {(au')(t) = b(t)f(t,u(t)), t subset of (0,1), u'(0)= u(1) =0, where a is an element of C-l((0,1),(0,infinity)), 1/a is integrable on any compact subset of (0,1 vertical bar ,b is an element of C((0, 1) , [0, + infinity)) does not vanish identically and is integrable on any compact subset of [0,1), and f : [0,1] x R-+,R- -> R+ is continuous with f(t, u) > 0 for all (t, u) is an element of [0,1] x (0, infinity). As applications, existence and nonexistence criteria for positive radial solutions to some elliptic equations are deduced.