一类含临界指标的双调和方程解的存在性

本文研究以下具有Navier边界,含临界指标的双调和方程解的存在性:{Δ2u=λ|u|q-2u+μ|u|2,-2u,x∈Ωu=Δu=0,x∈Ω}其中Ω为RN中一个包含原点的具有光滑边界的有界区域,N≥5;1<q<2;λ,μ>0;2*=2N/N-4为Sobolev临界指数。通过在Nehari流形上抽取PS序列,得到方程非平凡解的存在性。

In this paper,we are concerned with the following problem：{u=△u=0,x∈σΩ △^2u=λ｜u｜^q-2 u＋μ｜u｜^2＊-2u,x∈Ω Where Ω is a bounded domain containing the origin in RN with ,N ≥5;αΩis sufficiently smooth. 1 〈q 〈2;λ,μ〉0;2= 2N/N-4 is the critical Sobolev exponent.By extracting the PalaisSmale sequence in the Nehari manifold ,the existence of nontrivial solution to this equation is verified.