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| We consider the initial value problem for a semilinear elliptic equation with a dynamical boundary condition in the half space, which the space dimension is greater or equal to 2.
In this talk we prove that there is a critical exponent for the existence of positive solutions.
Furthermore, in the supercritical case we show that small solutions behave asymptotically like suitable multiples of the Poisson kernel.
Moreover, we determine the optimal slow decay at spatial infinity
for initial data giving rise to global bounded positive solutions. |
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