Abstract

We study existence, multiplicity, and the behavior, with respect to lambda, of positive radially symmetric solutions of -Delta u = lambda h(x, u) in annular domains in R-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. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim