Abstract
This chapter is devoted to the investigation of stability and boundedness results of equations with infinite memory. We shall first discuss, in Sections 6.1 to 6.3, FDE with infinite delay and develop, in the general setup of two different measures, criteria for stability and boundedness. Here we utilize the method of perturbing Lyapunov functions and obtain nonuniform stability properties under weaker assumptions. We shall then concentrate in Section 6.4, on NFDE with infinite memory. Extending Razumikhin's method in terms of the comparison principle, we offer sufficient conditions for various stability properties. Examples are provided to illustrate the results.
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© 1994 Springer Science+Business Media Dordrecht
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Lakshmikantham, V., Wen, L., Zhang, B. (1994). Stability and Boundedness for Equations with Infinite Delay. In: Theory of Differential Equations with Unbounded Delay. Mathematics and Its Applications, vol 298. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2606-3_6
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DOI: https://doi.org/10.1007/978-1-4615-2606-3_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6116-9
Online ISBN: 978-1-4615-2606-3
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