含临界位势的半线性双调和方程的正解

摘要

主要研究了一类含临界位势双调和问题.利用Hardy不等式得到一个仅与维数N有关的上限λ*,且当λ＜λ时,不管维数是一般的还是临界的,该问题都至少有一个正解.%In this paper, we mainly studied a sort of semilinear weighted critical polyharmonic equations. in the critical weighted situation, by using Hardy inequality we can get an upper limit λ* which is only related to the dimension N, and when λ< λ*, the problem has at least one positive solution regardless of whether the dimension is critical or not.