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A new nonlinear integro-differential inequality and its application

✍ Scribed by Daoyi Xu; Xiaohu Wang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
461 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this paper, a new nonlinear integro-differential inequality is established. Using the properties of M-cone and a generalization of Barbalat's lemma, the boundedness and asymptotic behavior for the solution of the inequality are obtained. Applying this nonlinear integro-differential inequality, the invariant and attracting sets for Cohen-Grossberg neural networks with mixed delays are obtained. The results extend and improve the earlier publications. An example is given to illustrate the efficiency of the obtained results.

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We consider a class of abstract evolutionary variational inequalities arising in the study of frictional contact problems for linear viscoelastic materials with long-term memory. First, we prove an abstract existence and uniqueness result, by using arguments of evolutionary variational inequalities