Several integral inequalities and their applications in nonlinear differential systems

被引:10
作者
Guo, Shuli [1 ,2 ]
Moroz, Irene [2 ]
Si, Ligeng [3 ]
Han, Lina [4 ]
机构
[1] Beijing Inst Technol, Sch Automat Control, Beijing 100081, Peoples R China
[2] Univ Oxford, Math Inst, Oxford OX1 3LB, England
[3] Inner Mongolia Normal Univ, Dept Math Sci, Hohhot 010022, Peoples R China
[4] Chinese PLA Hosp, Dept Cardiovasc Internal Med 1, Beijing 100853, Peoples R China
关键词
Nonlinear differential equation; Uniform Lipschitz stability; Uniform Lipschitz asymptotical stability; BIHARI TYPE INEQUALITIES; LIPSCHITZ STABILITY; DISCONTINUOUS FUNCTIONS; EQUATIONS;
D O I
10.1016/j.amc.2012.10.102
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, several new integral inequalities are presented, which are effective in dealing with the integro-differential inequalities whose variable exponents are greater than one. Compared with existing integral inequalities, those proposed here can be applied to more complicated differential equations. The notions of uniform Lipschitz stability are generalized and the relations between these notions are analyzed. Several sufficient conditions about uniform Lipschitz asymptotic stability of nonlinear systems are established by the proposed integral inequalities. These sufficiently conditions can be similarly generalized to linearly perturbed differential systems that appear in the literature. Finally, an example of uniform Lipschitz asymptotic stability of nonlinear differential systems is shown. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码:4266 / 4277
页数:12
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