摘要
本文在一般Ｂａｎａｃｈ空间Ｘ上研究抽象线性脉冲方程ｕ′（ｔ）＝Ａｕ（ｔ），ｔ≠０，ｔ∈Ｒ，△ｕ（０）＝ｘ，的可解范围．其中Ａ是闭线性算子，含于ρ（Ａ）文中构造了Ｘ的一个线性予空间Ｖ且在Ｖ上定义范数｜·｜，使（Ｖ，｜·｜）成为Ｂａｎａｃｈ空间，Ａ限制在Ｖ上生成指数衰减的强连续双半群，从而表明方程（＊）在Ｖ上可解，并证明Ｖ是（＊）可解的极大范围．
In this paper,we study the linear impulse equation on Banach space X u′(t)=Au(t),t≠0,t∈R, △u(0)=x,where A is a closed linear operator in X with domain D(A),with the set {λ∈C‖Reλ|< h} included in P(A) .We define a linear subspace V X and a norm|.| on V such that (V,|.|) is a Banach space and the restriction of A to V generates an exponentially decaying and strongly continuous bisemigroup.Therefore,the equation has a solution x in V .We show the subspace V is maximal in a certain sense.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1995年第1期71-80,共10页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
山西省青年科学基金
