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

Y. Ren () and D. D. Sun
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Y. Ren: Anhui Normal University
D. D. Sun: Anhui Normal University

Journal of Optimization Theory and Applications, 2010, vol. 147, issue 3, No 10, 569-582

Abstract: 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.

Keywords: Second-order neutral stochastic evolution equation; Cosine family; Infinite delay; Carathéodory condition (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-010-9727-9

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