Asymptotic behavior of positive solutions of some elliptic problems
Edward Norman Dancer, Yihong Du, Li Ma · Pacific Journal of Mathematics · 2003
In this paper, we discuss the asymptotic behavior of the positive solutions of the problem -∆u = au -bu p , u| ∂Ω = 0 as p → 1 + 0 and as p → ∞.We show that, for each case, the behavior is determined by a limiting problem.Moreover, the limiting problem is of free boundary nature when p → ∞.