Positive solutions for semilinear Dirichlet problems in an annulus (Q1181682)

This paper considers the existence of positive radial solutions of \(- \Delta u=g(| x|)f(u)\) in an annulus with zero boundary conditions. The main new idea here is to use the mountain pass lemma, which allows the proof of existence results in a simple, direct way when \(f\) is continuous. The case of discontinuous nonlinearities uses Chang's version of the mountain pass lemma for nonsmooth functionals.