一类半线性椭圆型方程爆炸解的存在性与渐近行为

ON THE EXISTENCE AND ASYMPTOTIC BAHAVIOR OF EXPLOSIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS

设Ω是RN（N2）中的C2有界区域，对非线性项带有适当的梯度与无界系数k（x），首先应用非线性变换将爆炸解问题，转化成等价的带奇异项的Dirichiet问题，应用极大值原理得到了爆炸解问题解的最小爆炸速度．随后，应用摄动方法，结合上下解方法与椭圆型方程的估计理论得到了爆炸解的存在性．

Let Ωbe a bounded domain with C2 boundary On in RN (N≥2), for the suitable gradient and unbounded coefficient k(x) of nonlinearity, the change of variable transforms the problem of explosive solutions into the equivalellt Dirichlet problem. It follows by the mtximum principle that the explosive solutions have the lowest speed. Moreover,by the perturbed method, combining sub-supersolutions method and the estimates theorey for elliptic equations of second order, the existence of explosive solutions is obtained.