Positive solutions for an elliptic equation in an annulus with a superlinear nonlinearity with zeros

We study existence, multiplicity, and the behavior, with respect to λ, of positive radially symmetric solutions of − Δ u = λ h ( x , u ) in annular domains inR N ,N ≥ 2 . The nonlinear term has a superlinear local growth at infinity, is nonnegative, and satisfies h ( x , a ( x ) ) = 0for a suitable positive and concave function a . For this, we combine several methods such as the sub and supersolutions method, a priori estimates and degree theory.