MULTIPLE POSITIVE SOLUTIONS FOR SINGULAR m-POINT BOUNDARY-VALUE PROBLEMS WITH NONLINEARITIES DEPENDING ON THE DERIVATIVE.

nUsing the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular m-point boundary-value problem x"(t)+a(t)f(t,x(t), x' (t)) = 0, 0<t<1, x'(0) = 0, x(1) = m-2∑i=1aix(ξi), where 0 < ξ1 < ξ2 < ... < ξm-2 < 1, ai ∈ [0, 1), i = 1, 2, ... ,m - 2, with 0 > ∑i=1m-2ai < 1 and f maybe singular at x = 0 and x' = 0. [ABSTRACT FROM AUTHOR]