一类拟线性椭圆方程整体解的不存在性

The nonexistence of entire solutions for a class of quasilinear elliptic equation

这篇文章主要利用常微分技术讨论了一个二阶拟线性椭圆方程Lpu≡div(|Du|p-2Du)=f(x,u),x∈RN的整体解的不存在性.我们只考虑2≤p<N的情况并且在假设f(x,u)关于第二个变量u没有单调性的情况下得到整体解的不存在性结果.

In this paper,by virtue of ordinary-differential-equation technique,we get the nonexistence of entire solutions for a class of second-order quasilinear elliptic equations Lpu ≡ div（｜Du｜^p-2Du） = f（x,u） ,x ∈ R^N. We only consider the case of 2 ≤ p 〈 N and show that the main condition for the nonexistence of the solution is the nonmonotonity property of f（x,u） with respect to the second variable u.