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

Arcoya, D.

J. Differ. Equations 94, No. 2, 217-227 (1991).

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.

Reviewer: S.Lenhart (Knoxville)

MSC:

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

Keywords:

mountain pass lemma; existence results; discontinuous nonlinearities

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