临界指数半线性重调和方程NAVIER边值问题非平凡解的存在性

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR NAVIER BOUNDARY VALUE PROBLEMS OF SEMILINEAR BIHARMONIC EQUATIONS INVOVING CRITICAL SOBLOV EXPONCNTS

本文我们研究下列方程：Δ２ｕ＝｜ｕ｜ｐ－１ｕ＋ｆ（ｘ，ｕ）ｘ∈Ωｕ＝０ｘ∈ΩΔｕ＋α（ｘ）ｕｖ＝０ｘ∈Ω的非平凡解存在性，这里ｐ＝（ｎ＋４）／（ｎ－４），ｆ（ｘ，ｕ）是｜ｕ｜ｐ－１ｕ在无穷远处的低阶扰动项，ｆ（ｘ，０）＝０，并且。

In this paper we study the existence of nontrivial solutions to the following Navier problem: Δ 2u=|u| p-1 u+f(x,u)\ x∈Ω u=0 x∈Ω Δu+α(x)uv=0\ x∈Ω where p=(n+4)/(n-4),f(x,u)is a lower order perturbation of |u| p-1 u at infinity,f(x,0)=0.Then we obtain a general existence theorem.