摘要
本文研究初边值问题其中Ω是R^n中的有界区域,A=-△是定义在A=-△上的Laplace算子.利用位势井方法得到了解的存在性定理,并且证明了当e∈(0,d)时,以E(0)∈(0,e]为初始能量的所有解只能位于空间D(A^(1/2))中小球的外部和大球的内部,其中,C_*是空间D(A^(1/2))到L^(p+1)(Ω)的嵌入常数.
In this paper, the initial boundary value problem is studied, where Ω C R^N is a bounded domain, A = -△ is the Laplace operator with the domain D(A) = H2(Ω)∩H0^1(Ω). By using the potential well method, one obtains some existence theorems of solutions, and proves that for any given e ∈ (0, d) all solutions with initial energy E(0) 6 (0, e) can only lie either inside of some smaller ball or outside of some bigger ball of space D(A^1/2), where d=p-2γ-1/(2γ+2)(p+1)(1/C*^p+1)^2γ+2/p-1-2γ and C, is the imbedding constant from D(A^1/2) into L^p+1 (Ω).
出处
《数学进展》
CSCD
北大核心
2013年第4期511-516,共6页
Advances in Mathematics(China)
基金
This work is supported by NSFC(No.11271336)