一类临界指数增长的椭圆型方程组正解的存在性

摘要

研究了一类临界指数增长的椭圆型方程组。通过变分法，得到方程组的能量泛函在零点附近的局部极小值点的存在性，且该极小值点为方程组的正解。证明了当方程组的扰动项趋于零时，方程组的正解也趋于零。%This paper studies an elliptic system involving Sobolev critical exponent. By the variational methods, we can obtain the existence of local minimum point of the energy functional related to the system which is near zero, and the local minimum point is the positive solution to this system. Moreover, It is also proved that this positive solution tends to zero when the perturbed term goes to zero.