Qualitative properties for the Laplace equation with a dynamical boundary condition

研究了一类具有非线性动力边界条件的拉普拉斯方程和一类具有动力边界条件的非线性椭圆型方程的正解在半空间中的大时性。我们确定了正解全局存在的一个临界指数，并证明了小解的行为就像泊松核的合适倍数。

We studied the large time behavior of positive solutions for the Laplace equation with a nonlinear dynamical boundary condition and for a nonlinear elliptic equation with a dynamical boundary condition, in a half space. We identified a critical exponent for the global existence of positive solutions and showed that small solutions behave likesuitable multiples of the Poisson kernel.