Differential and Integral Equations

On stochastic delay evolution equations with non-lipschitz nonlinearities in Hilbert spaces

T.E. Govindan

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Abstract

In this paper, we study existence and exponential stability problems of mild solutions associated with stochastic delay evolution equations in Hilbert spaces. These problems are resolved using the properties of a stochastic convolution integral and a comparison principle by exploiting Holder-type conditions on the drift and diffusion terms. The results obtained here generalize the corresponding main results from [1, 3, 4, 9, 13, 16].

Article information

Source
Differential Integral Equations Volume 22, Number 1/2 (2009), 157-176.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038559

Mathematical Reviews number (MathSciNet)
MR2483017

Zentralblatt MATH identifier
1240.60181

Subjects
Primary: 60H20: Stochastic integral equations 34K50: Stochastic functional-differential equations [See also , 60Hxx] 93E15: Stochastic stability

Citation

Govindan, T.E. On stochastic delay evolution equations with non-lipschitz nonlinearities in Hilbert spaces. Differential Integral Equations 22 (2009), no. 1/2, 157--176. https://projecteuclid.org/euclid.die/1356038559.


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