关于某些二阶Elliptic Differential Equations的注记
Some Remarks on Some Second-Order Elliptic Differential Equations
摘要：
研究了$\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$型二阶椭圆型微分方程的概自守解，其中$A, B$是作用在希尔伯特空间${\mathbb H}$上的稠密闭线性算子，$f: {\mathbb R} \mapsto {\mathbb H}$是向量值概自守函数.使用不变子空间，它将表明，在适当的假设下，每个解决方案，$(\ast)$几乎是自守的。
英文摘要：
We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$ where $A, B$ are densely defined closed linear operators acting in a Hilbert space ${\mathbb H}$ and $f: {\mathbb R} \mapsto {\mathbb H}$ is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions; every solution to $(\ast)$ is almost automorphic.
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