MULTIPLICITY RESULTS OF POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEMS WITH TIME DEPENDENT NONLINEARITY

We investigate bifurcation phenomena of positive solutions for problems of the form; u 00(t) + λf(t, u(t)) = 0, t ∈ (0, 1), u(0) = 0 = u(1), when f satisfies that there exists r ∈ C((0, 1),(0, ∞)) with R1 0 s(1 − s)r(s)ds < ∞ such that 0 < limu→0+ f(t,u) r(t)u < ∞ uniformly in t ∈ (0, 1). Here λ is a positive real parameter and f ∈ C((0, 1) × [0, ∞), [0, ∞)) may be singular at t = 0 and/or t = 1.