Second-order neutral impulsive stochastic evolution equations with delay. (English) Zbl 1236.60057
Summary: In this paper, we study the second-order neutral stochastic evolution equations with impulsive effect and delay (SNSEEIDs). We establish the existence and uniqueness of mild solutions to SNSEEIDs under non-Lipschitz condition with Lipschitz condition being considered as a special case by the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial data by means of corollary of the Bihari inequality. An application to the stochastic nonlinear wave equation with impulsive effect and delay is given to illustrate the theory.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34K50 | Stochastic functional-differential equations |
| 34K30 | Functional-differential equations in abstract spaces |
| 34K40 | Neutral functional-differential equations |
| 34K45 | Functional-differential equations with impulses |
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