R^N上具有临界指标的重调和方程非平凡解的存在性

Existence of Nontrivial Solutions for Biharmonic Equation with Critical Exponent in R^N

运用扰动方法研究RN(N>4)上具有临界指标的重调和方程{Δ2u=uN+4/N-4+εg(χ,u),limu|x|→∞(x)=0,u∈D2,2(RN),χ∈RN非平凡解的存在性,其中ε为任意小常数,lim|x|→∞g(χ,u)=0.

Mainly study the existence of nontrivial solutions for a biharmonic equation with critical exponert in R^N（N 〉 4） as {△^2u=uN＋4/N-4＋εg（x,u）,limu｜x｜→∞（x）=0,u∈D^2.2（R^N）,x∈R^N where e is a small constant, limg｜x｜→∞（x, u） = 0.