含临界位势的半线性双调和方程的正解(英文)

The Positive Solution of Semilinear Biharmonic Equation with Critical Weight

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.