一带权多重调和方程正解的存在性及渐近行为  

Existence and Asymptotic Behaviour of Positive Solutions for a Polyharmonic Equation with Weight

作　　者：王中亮[1,2] 

机构地区：[1]第二军医大学数理教研室,上海200433 [2]华东师范大学数学系,上海200241

出　　处：《数学物理学报（A辑）》2013年第5期829-841,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(10971067)资助

摘　　要：通过建立径向对称解的先验估计,并运用Pohozaev型恒等式研究多重调和方程{(-△)mμ=︱χ︱αμp-1,μ>0,在B中,Diμ︱αB=0,︱i︱≤m-1解的存在性,其中m∈N,B是R^n中单位球,n≥2m+1,α>0且p>2.进一步,运用Blow-up分析获得上述方程当α固定及p→2n/(n-2m)时,最小能量解的渐近行为.In this paper,the author establishes a prior estimate of the radially symmetric solutions,and apply a Pohozaev-type identity to the research on the existence of solutions for the polyharmonic equation {（-△）mu =｜x｜αup-1,u ＞ 0,in B,Diu｜（δ）B =0,｜i｜ ≤ m-1,where m ∈ N,B is the unit ball in Rn with n ≥ 2m＋ 1,α ＞ 0 and p ＞ 2.Moreover,by making use of the Blow-up analysis,the asymptotic behaviour of the least energy solutions for above equation is obtained when α is fixed and p → 2n/（n-2m）.

关 键 词：多重调和方程 SOBOLEV临界指数 径向对称解 渐近行为 对称破裂 

分 类 号：O175.4[理学—数学]