Brown, K. J.; Hess, P. Stability and uniqueness of positive solutions for a semi-linear elliptic boundary value problem. (English) Zbl 0729.35046 Differ. Integral Equ. 3, No. 2, 201-207 (1990). The authors examine solutions of the semilinear boundary value problem (*) \(-\Delta u=g(x)f(u)\) in D, \(Bu=0\) on \(\partial D\), where D is a smooth bounded domain in \({\mathbb{R}}^ n\) and B denotes Dirichlet, Neumann, or Robin boundary conditions. Suppose also that f is strictly concave, that \(f(0)=0\), and that f is sublinear at infinity or vanishes at some finite number. Under suitable conditions on g, which allow g to change sign, the authors determine the number of positive solutions of (*); this number will be zero or one. Reviewer: G.M.Lieberman (Ames) Cited in 1 ReviewCited in 35 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B35 Stability in context of PDEs Keywords:semilinear boundary value problem; Dirichlet, Neumann, or Robin boundary conditions PDF BibTeX XML Cite \textit{K. J. Brown} and \textit{P. Hess}, Differ. Integral Equ. 3, No. 2, 201--207 (1990; Zbl 0729.35046) OpenURL