一类奇异超线性椭圆方程解增长速度估计

Growth estimates of a singular super-linear elliptic equation

讨论边界奇异超线性方程:-Δu=a(x)up,x∈RN,其中连续函数a(x)=η(x)[d(x,Ω)]γ,η(x)≥0,γ>0。运用一个新的非线性Liouville定理讨论了当函数a(x)在光滑有界区域Ω上为0,而在RN\Ω珚上为正时,方程正解的估计问题,得到了相应于当a(x)≡1时方程正解估计的可比较性结果。

The boundary estimates of the singular superlinear elliptic equation -△U=a（x）u^p,X∈R^N, is considered, where continuous function a（x）=η（x）[d（x,δΩ）]^γ,η（x）≥0,γ〉0, When a（x） ≡0 in a smooth bounded subdomain Ω, and positive in R^N ／Ω. By using a new nonlinear Liouville theorem, an estimate of the positive solution comparable is obtained for those in a（x） ≡1 case.