指数型非线性椭圆方程解的渐近行为

Asymptotic Behavior of an Exponential Nonlinear Elliptic Equation Solution

摘要: 本文主要研究的是六阶指数型非线性椭圆方程, 该方程为负的拉普拉斯算子的三次方作用于 u(x) 等于 e 的 u(x) 次方. e 的 u(x) 次方函数在 R 的六维空间去掉一个单位球 B 的区域上是勒贝格 可积的, 其中单位球 B 是由 R 六维空间中满足 x 的模小于 1 的所有 x 组成. 当 x 的模趋于无穷 大的时候, u(x)/ ln |x| 的极限是 α, 其中 α 小于 -6.

Abstract: This paper mainly studies the sixth-order exponential nonlinear elliptic equation, which is the cube of the negative Laplacian acting on u equal to e to the power of u. The function e to the power of u(x) is Lebesgue integrable in the region of the six-dimensional space of R excluding a unit ball B, where the unit ball B is composed of all x in the six-dimensional space of R satisfying the modulus of x is less than 1. When the modulus of x tends to infinity, the limit of u(x)/ ln |x| is α, where α is less than -6.