有界域上带梯度项非线性椭圆型方程的正爆破解

Existence of Positive Explosive Solutions of Nonlinear Elliptic Equations with Gradient Term

设Ω是RN(N ≥3)中的C2类有界区域,针对变号函数的情形,研究了一类带梯度项的非线性椭圆型方程在Ω上正爆破解的存在性.应用上下解方法并结合二阶椭圆型偏微分方程的内估计理论,得到了正爆破解存在的若干充分性条件,部分推广了原有结果.

Let Ω belong to R^N （N ≥ 3） be a C^2 bounded domain, when the gradient term contains coeffcient functions which does not hold the same symbol, the existence of positive explosive solutions of nonlinear elliptic equation in Ω are considered. Some sets of suitable conditions are given by using the explosive super-subsolution method and Schauder inner estimation theory, which guarantee the existence of explosive positive solutions respectively.