Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Neutral Functional Differential Equations with Infinite Delays

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.

[1]  I. Bihari A generalization of a lemma of bellman and its application to uniqueness problems of differential equations , 1956 .

[2]  V. Kolmanovsky,et al.  Stability of neutral-type functional differential equations , 1982 .

[3]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[4]  On existence and uniqueness of solution of stochastic differential equations with heredity , 1984 .

[5]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[6]  A. Samoilenko,et al.  Impulsive differential equations , 1995 .

[7]  Hernán R. Henríquez,et al.  Existence results for partial neutral functional differential equations with unbounded delay , 1998 .

[8]  A. Myshkis,et al.  Stability of Neutral Type Functional Differential Equations , 1999 .

[9]  T. E. Govindan,et al.  Stability of Mild Solutions of Stochastic Evolution Equations with Variable Delay , 2001 .

[10]  An existence result for the Cauchy problem for stochastic systems with heredity , 2002 .

[11]  乔花玲,et al.  关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解 , 2003 .

[12]  Shujin Wu,et al.  Existence and Uniqueness of Solutions to Random Impulsive Differential Systems , 2006 .

[13]  T. Kurtz,et al.  Stochastic equations in infinite dimensions , 2006 .

[14]  Zhiguo Yang,et al.  Exponential p-stability of impulsive stochastic differential equations with delays , 2006 .

[15]  A. Anguraj,et al.  Existence results for an impulsive neutral functional differential equation with state-dependent delay , 2007 .

[16]  Hernán R. Henríquez,et al.  Existence of solutions for impulsive partial neutral functional differential equations , 2007 .

[17]  Shouming Zhong,et al.  Mean square stability analysis of impulsive stochastic differential equations with delays , 2008 .

[18]  Yong Ren,et al.  Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay , 2008 .

[19]  Liu Ming-zhu Exponential p-stability of impulsive stochastic differential equations with delays , 2009 .

[20]  R. Sakthivel,et al.  Asymptotic stability of nonlinear impulsive stochastic differential equations , 2009 .

[21]  Yong Ren,et al.  Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay , 2009, Appl. Math. Comput..

[22]  Donal O'Regan,et al.  Existence results for abstract neutral functional differential equations , 2009 .

[23]  R. Sakthivel,et al.  Asymptotic stability of impulsive stochastic partial differential equations with infinite delays , 2009 .

[24]  Jianhai Bao,et al.  Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients , 2010, Comput. Math. Appl..

[25]  Existence, Uniqueness and Stability Results of Impulsive Stochastic Semilinear Functional Differential Equations with Infinite Delays , 2011 .