双调和方程上下解定理及其应用

THE BARRIER THEOREM OF A BIHARMONIC PROBLEM AND APPLICATION

给出了下列边值问题：Δ２ｕ＝ｇ（ｘ，ｕ），ｘ∈Ω，ｕ｜Ω＝０，ｕｎΩ＝０｛的上下解定理，其中ΩＲＮ是有界光滑区域，ｇ（ｘ，ｕ）关于ｕ连续，关于ｘ可测；并讨论了临界非齐次双调和方程解的存在性．

This paper gives the barrier theorem of the following biharmonic problem :Δ 2u=g(x,u), x∈Ω, u|  Ω =0,  u n  Ω =0,where Ω is a bounded no empty smooth domain in R N; g(x,u) is continuous with respect to u, and measurable with respect to x; and n is the outward unit normal to  Ω. Furthermore, this paper discusses the existence of the solution for a critical inhomogeneous biharmonic problem.