带有临界Sobolev-Hardy指数的非齐次椭圆方程解的存在性

Existence of solution for nonhomogeneous elliptic eqution involving critical Sobolev-Hardy exponents

运用偏微分方程的变分方法和 Sobolev-Hardy不等式 ,讨论了一类具有奇异系数和临界Sobolev-Hardy指数的非齐次二阶椭圆方程 ,证明了在一定条件下方程至少存在一个解 。

This paper discusses a nonhomogeneous elliptic equation involving singular coefficient and critical Sobolev Hardy exponent by variational method in PDE and Sobolev Hardy inequality. Under certain condition, there proves the existence of at least one solution to the equation, which is a local minimizer of the energy functional.