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Second-order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions

Author

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  • Y. Ren

    (Anhui Normal University)

  • D. D. Sun

    (Anhui Normal University)

Abstract

In this paper, we study a class of second-order neutral stochastic evolution equations with infinite delay, in which the initial value belongs to the abstract space ℬ. We establish the existence and uniqueness of mild solutions for SNSEEIs under global and local Carathéodory conditions by means of the successive approximation. An application to the stochastic nonlinear wave equations with infinite delay is given to illustrate the theory.

Suggested Citation

  • Y. Ren & D. D. Sun, 2010. "Second-order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 569-582, December.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9727-9
    DOI: 10.1007/s10957-010-9727-9
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    References listed on IDEAS

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    1. P. Balasubramaniam & P. Muthukumar, 2009. "Approximate Controllability of Second-Order Stochastic Distributed Implicit Functional Differential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 225-244, November.
    2. Caraballo, Tomás & Liu, Kai, 1999. "On exponential stability criteria of stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 289-301, October.
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    Cited by:

    1. Ren, Yong & Hou, Tingting & Sakthivel, R. & Cheng, Xing, 2014. "A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 658-665.
    2. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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