Comparison Theorems of Liapunov-Razumikhin Type for NFDEs With Infinite Delay

Haddock, John R. ; Ruan, Shigui ; Wu, Jianhong ; Xia, Huaxing

Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 500-526

Résumé

Some comparison theorems of Liapunov-Razumikhin type are provided for uniform (asymptotic) stability and uniform (ultimate) boundedness of solutions to neutral functional differential equations with infinite delay with respect to a given phase space pair. Examples are given to illustrate how the comparison theorems and stability and boundedness of solutions depend on the choice(s) of phase space(s) and are related to asymptotic behavior of solutions to some difference and integral equations.

Détail

DOI : 10.4153/CJM-1995-028-7

Mots-clés : 34K40, 34K20, 34D40, stability and boundedness, Liapunov-Razumikhin technique, NFDEs with infinite delay, comparison method

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