We consider the semilinear elliptic equation – Δu = up, p > 1, u = u (x,t) x ∈ ℝN+, t > 0, with a dynamical boundary condition. We show that, for p < (N+1)/(N-1), there exist no nontrivial nonnegative local-in-time solutions. Furthermore, in the case P > (N+1)/(N-1)$$p>(N+1)/(N-1), we determine the optimal slow decay rate at spatial infinity for initial data giving rise to global bounded positive solutions.
|Number of pages||20|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2015 Oct 22|
ASJC Scopus subject areas
- Applied Mathematics