圆环区域上带梯度项的椭圆型方程径向大解的爆破速率

The Blow-up Rates of Large Radial Solutions for the Elliptic Equation with Gradient Term in Annular

本文研究在圆环区域上带梯度项和完全非线性项的半线性椭圆型方程边值问题径向大解的爆破速率。在证明一些重要极限的基础上,与常微分方程分析法相结合得到了当完全非线性项满足Keller-Osserman条件,梯度项的指数范围分别在0～1和大于2时径向大解的爆破速率及在加强的条件下大解边界行为的第二次影响.

In this paper,the blow-up rates of large radial solutions for the semilinear elliptic equation with gradient term and fully nonlinear term in annular domain was investigated.On the basis of the proof of some important limits,using ordinary differential equation analysis method,we achieved the blow-up rates of large radial solutions when fully nonlinear term satisfies the Keller-Osserman conditions and the exponential of gradient term ranges from 0 to 1 or larger than 2.Moreover,we considered a secondary effect on the asymptotic behavior of solutions under the enhanced conditions.