一类椭圆型方程爆炸解的存在性

The existence of the explosive solutions for a class of quasilinear elliptic equations

在RN(N≥2)中的C2有界区域上,对带有适当梯度的非线性项半线性椭圆型方程爆炸解存在性的研究已有许多.在此基础上,考虑RN(N≥3)中含有梯度项的二阶拟线性椭圆型方程解的存在性问题,利用球形区域上爆炸解的逼近方法,结合下解方法得到了爆炸解的存在性.

Many researchers had solved the existence of explosive solution for semilinear elliptic equation in a bounded domain with C^2 boundary δΩ in R^N（N≥2） with a suitable gradient nonlinearity. It was discussed the existence for a class of quasilinear elliptic equation with gradient nonlinearity in R^N（N≥2）. The existence of the explosive solution for quasilinear elliptic equation was given by means of approximating in sphere and subsolution method.