We consider the superlinear boundary value problem
u'' +a_μ (t)u^(g+1)u=0,
u(0) = 0, u(1) = 0,
where
g> 0 and a_μ(t) is a sign indefinite weight of the form a+(t)−μa−(t). We
prove, for μ positive and large, the existence of 2k − 1 positive solutions where k
is the number of positive humps of aμ(t) which are separated by k − 1 negative
humps. For sake of simplicity, the proof is carried on for the case k = 3 yielding
to 7 positive solutions. Our main argument combines a modified shooting method
in the phase plane with some properties of the blow up solutions in the intervals
where the weight function is negative.
