摘要
本文讨论如下类型的高阶抽象Cauchy问题其中A为一Banach空间E中的线性算子,n≥3.我们指明了:设存在r>0,使得[r,∞)<ρ(A),如果存在某一k∈{1,2,3,……}及一特殊集合[D(A^k)]~n=D(A^k)×D(A^k)×…D(A^k),使对任意的(u_0,u_1,…u_(n-1))∈[D(A^k)]~n,(ACP_n)均存在唯一的O(e^(rt))解,则A必为有界线性算子。从而,我们得知:若存在r>0使得[r,∞)∈p(A),则(ACP_n)O(e^(rt))解存在唯一(对某初值域)的充分必要条件是A为有界算子。
This paper investigates the following types of higher order abstract Cauchy problems: where A is a linear operator on a Banach space E, n>3. We point out that, if[r, ∞)<ρ(A) for some r>0, and there is a k∈ {1,2,3,…} such that for each (u_0, u_1…, u_(n-1))∈[D(A^k)]~n=D(A^k)×…×D(A^k), (ACP_n) has a unique O(e^(rt)) solution, then A is bounded. Thus, We know that assuming [r,∞)<ρ(A) for some r>0, then a sufficient and necessary condition for the existence of a unique O(e^(rt)) solution of (ACP_n) (for some set of initial data) is that A is a bounded operator.
出处
《云南师范大学学报（自然科学版）》
1993年第3期1-7,共7页
Journal of Yunnan Normal University:Natural Sciences Edition
基金
国家自然科学青年基金
云南省应用基础研究基金
关键词
初值问题
微分方程
巴拿赫空间
(ACP_n) O(e^(rt)) Existence and uniquencess Bounded
