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Uniform exponential stability of solutions to abstract Volterra equations

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In terms of the spectral properties of the associated operator matrix, we obtain a new criterion to judge the uniform exponential stability of the solutions to abstract Volterra equations. In particular, we study in detail the case where the kernel function a(t) takes the form α e βt (β > 0, α ≠ 0). Moreover, we give examples to illustrate our results.

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Correspondence to Ti-Jun Xiao.

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The work was supported partly by the NSF of China (10771202), the Research Fund for Shanghai Key Laboratory of Modern Applied Mathematics (08DZ2271900) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (2007035805).

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Chen, JH., Xiao, TJ. & Liang, J. Uniform exponential stability of solutions to abstract Volterra equations. J. Evol. Equ. 9, 661 (2009).

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