含奇异权函数的椭圆方程组边界爆破解的唯一性(Uniqueness of boundary blow-up solution to an elliptic system with singular weights)

Abstract

Based on the construction of certain upper and sub-solutions, the boundary behavior of positive boundary blow-up solutions to elliptic systems are obtained， here the singular weight functions b1(x),b2(x) are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts. Furthermore, the uniqueness of the boundary blow-up solutions without the exact boundary behavior are also studied. The results show that it is not necessary to impose an exact boundary behavior to the weight functions, but only to control their growth near the boundary for uniqueness.

Keywords

• elliptic system
• upper and sub-solutions
• boundary blow-up