Abstract
This article presents the results on existence, uniqueness and stability of mild solutions of impulsive stochastic semilinear neutral functional differential equations without a Lipschitz condition and with a Lipschitz condition. The results are obtained by using the method of successive approximations. 2000 Mathematical Subject Classification: 93E15,60H15,35R12.
Highlights
Neutral differential equations arise in many area of science and engineering and have received much attention in the last decades
The ordinary neutral differential equation is used extensively to study the theory of aeroelasticity [10] and lossless transmission lines
Partial neutral differential equations with delays are motivated from stabilization of lumped control systems and the theory of heat conduction in materials
Summary
Neutral differential equations arise in many area of science and engineering and have received much attention in the last decades. Partial neutral differential equations with delays are motivated from stabilization of lumped control systems and the theory of heat conduction in materials (see [7; 8] and the references therein). In [15; 4], the authors studied several existence results of stochastic differential equations (SDEs) with unbounded delays. The study of impulsive stochastic differential equations (ISDEs) is a new area of research and few publications on that subject can be found. 1 the existence and asymptotic stability in p-th moment of mild solutions to ISDEs with and without infinite delays through fixed point theory. Motivated by [13; 14], we generalize the existence and uniqueness of the solution to impulsive stochastic partial neutral functional differential equations (ISNFDEs) under non-Lipschitz conditions and under Lipschitz conditions.
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