We study the following nonlinear critical elliptic equation

where \(\epsilon >0\) is small and \(N\ge 5.\) Assuming that Q(y) is periodic in \(y_1\) with period 1 and has a local minimum at 0 satisfying \(Q(0)>0,\) we prove the existence and local uniqueness of infinitely many bubbling solutions of it. This local uniqueness result implies that some bubbling solutions preserve the symmetry of the potential function Q(y), i.e., the bubbling solution whose blow-up set is \(\{(jL,0,\ldots ,0):j=0,\pm 1, \pm 2,\ldots , \pm m\}\) must be periodic in \(y_{1}\) provided that \(\epsilon \) goes to zero and L is any positive integer, where m is the number of the bubbles which is large enough but independent of \(\epsilon .\)

我们研究如下非线性临界椭圆方程

其中\(\epsilon >0\)很小且\(N\ge 5.\)假设Q ( y ) 在\(y_1\)中是周期性的，周期为 1 并且在 0 处有一个局部最小值满足\(Q( 0)>0,\)证明了它的无限多冒泡解的存在性和局部唯一性。这个局部唯一性结果意味着一些冒泡解保留了势函数Q ( y ) 的对称性，即冒泡解的爆炸集是\(\{(jL,0,\ldots ,0):j=0 ,\pm 1, \pm 2,\ldots , \pm m\}\)在\(y_{1}\)中必须是周期性的，前提是\(\epsilon \)变为零且L是任何正整数，其中m是足够大但与\(\epsilon .\)无关的气泡数