【摘要】 本文研究初边值问题其中Ω是Rⁿ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.更多还原

【Abstract】 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）∩H₀¹（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） ∈(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=（?）and C,is the imbedding constant from D(A^1/2) into L^p+1（Ω）.更多还原