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Exponential stability for abstract linear autonomous functional differential equations with infinite delay

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  • Jin Liang
  • Falun Huang
  • Tijun Xiao

Abstract

Based on our preceding paper, this note is concerned with the exponential stability of the solution semigroup for the abstract linear autonomous functional differential equation x ˙ ( t ) = L ( x t ) ( ∗ ) where L is a continuous linear operator on some abstract phase space B into a Banach space E . We prove that the solution semigroup of ( ∗ ) is exponentially stable if and only if the fundamental operator ( ∗ ) is exponentially stable and the phase space B is an exponentially fading memory space.

Suggested Citation

  • Jin Liang & Falun Huang & Tijun Xiao, 1998. "Exponential stability for abstract linear autonomous functional differential equations with infinite delay," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 21, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:549151
    DOI: 10.1155/S0161171298000362
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