Abstract
We consider the boundary value problem \[ − Δ u = f ( u ) in Ω , B u = 0 on ∂ Ω , - \Delta u = f(u)\,{\text {in}}\,\Omega {\text {,}}Bu = 0\,{\text {on}}\,\partial \Omega , \] where Ω \Omega is a bounded region in R n {\mathbb {R}^n} with smooth boundary. We prove stability and instability results of positive solutions under various choices of f f .
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