Nonlinear impulsive systems on infinite dimensional spaces

被引:60
作者
Ahmed, NU
Tea, KL
Hou, SH
机构
[1] Univ Ottawa, Sch Informat Technol & Engn, Dept Math, Ottawa, ON K1N 6N5, Canada
[2] Hong Kong Polytech Univ, Dept Math Appl, Hong Kong, Hong Kong, Peoples R China
关键词
nonlinear; impulsive; systems; infinite dimensional spaces; signed measures; vector measures; embedding;
D O I
10.1016/S0362-546X(03)00117-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we consider two different classes of nonlinear impulsive systems one driven purely by Dirac measures at a fixed set of points and the second driven by signed measures. The later class is easily extended to systems driven by general vector measures. The principal nonlinear operator is monotone hemicontinuous and coercive with respect to certain triple of Banach spaces called Gelfand triple. The other nonlinear operators are more regular, non-monotone continuous operators with respect to suitable Banach spaces. We present here a new result on compact embedding of the space of vector-valued functions of bounded variation and then use this result to prove two new results on existence and regularity properties of solutions for impulsive systems described above. The new embedding result covers the well-known embedding result due to Aubin. (C) 2003 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:907 / 925
页数:19
相关论文
共 14 条
[1]  
Ahmed N.U, 1995, DISCUSS MATH DIFFER, V15, P21
[2]   Necessary conditions of optimality for impulsive systems on Banach spaces [J].
Ahmed, NU .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (03) :409-424
[3]  
Ahmed NU, 2001, NONLINEAR ANAL-THEOR, V47, P13
[4]  
Ahmed NU, 2001, DYNAM CONT DIS SER B, V8, P251
[5]  
Ahmed NU, 2001, DYNAM CONT DIS SER A, V8, P261
[6]   Systems governed by impulsive differential inclusions on Hilbert spaces [J].
Ahmed, NU .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 45 (06) :693-706
[7]  
AHMED NU, 2002, NONLINEAR FUNCT ANAL, V7, P437
[8]  
Ahmed NU., 1981, Optimal Control of Distributed Parameter Systems
[9]  
AHMED NU, 2000, NONLINEAR FUNCT ANAL, V5, P96
[10]  
LAKSHMIKANTHAM V, 1999, THEORY IMPULSIVE DIF