Positive solutions for semilinear Dirichlet problems in an annulus. (English) Zbl 0768.35029

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.


35J65 Nonlinear boundary value problems for linear elliptic equations
35J20 Variational methods for second-order elliptic equations
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