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 ?, of positive radially symmetric solutions of -?u = ?h(x, u) in annular domains in RN,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. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.