摘要
考虑如下具有振动背景的带参数λ的四阶非对称微分算子A_λ及其一般化A_λ:(它们的定义在下面0、节给出)作者在文[1]中详细讨论了A_λ在四种(i,j)=((0,1),(0,2),(1,3),(2,3))场合的——有界性。本文将大大拓展讨论范围,即将文[1]中的先验估计方法与泛函分析的方法结合起来使用,不仅得到了A_λ的一般化A_λ——有界的结果,还得到了更确切地反映平稳性状的A_λ的正则性结果.特别地,本文还得到反映近似解性状的A_λ的扩张同构及在新拓扑下的同构.
This paper deals with the following four-order nonsymmetric differential operators λ? with parameter λ, and its general form Aλ arising from viberation problemsWe shall give the one-to-one bounded property and regularity property of Aλ, via the techniques of estimation and functional analysis. In particular, we shall obtain the ap-proximation solutions and new isomorphism for the extension isomorphism after endow the spaces with some new topologies.
