Qualitative properties for the Laplace equation with a dynamical boundary condition

研究了半空间中具有非线性动力边界条件的拉普拉斯方程和具有动力边界条件的非线性椭圆型方程正解的长时间行为.我们确定了一个临界指数的整体存在的正解，并表明，小的解决方案的行为likesuitable倍的泊松核。

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.