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

Abstract

We study existence, multiplicity, and the behavior, with respect to λ, of positive radially symmetric solutions of − 'delta'u = λh(x, u) in annular domains in 'R POT.N', N ≥ 2. The nonlinear term has a superlinear local growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for 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.