Existence results for impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions

In this paper, we prove the existence of mild solutions for a class of impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions and resolvent operators. Sufficient conditions for the existence are derived with the help of the fixed point theorem for multi-valued operators due to Dhage and the fractional power of operators. An example is provided to illustrate the theory.

[1]  Xianlong Fu,et al.  Existence for neutral impulsive differential inclusions with nonlocal conditions , 2008 .

[2]  Yong-Kui Chang,et al.  Existence results for impulsive neutral functional differential equations with infinite delay , 2008 .

[3]  J. Nieto,et al.  Existence of Solutions for Impulsive Neutral Integro-Differential Inclusions with Nonlocal Initial Conditions via Fractional Operators , 2009 .

[4]  Xianlong Fu,et al.  Existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions , 2004 .

[5]  Yong Ren,et al.  Existence Results for Impulsive Neutral Stochastic Functional Integro-Differential Equations with Infinite Delays , 2010 .

[6]  K. Deimling.  Multivalued Differential Equations , 1992 .

[7]  K. Deng.  Exponential Decay of Solutions of Semilinear Parabolic Equations with Nonlocal Initial Conditions , 1993 .

[8]  Toshiki Naito,et al.  Functional Differential Equations With Infinite Delay , 1991 .

[9]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[10]  K. Balachandran,et al.  Existence results for impulsive neutral functional integrodifferential equations with infinite delay , 2009 .

[11]  Yong-Kui Chang,et al.  Controllability of impulsive functional differential systems with infinite delay in Banach spaces , 2007 .

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

[13]  M. Benchohra,et al.  EXISTENCE AND CONTROLLABILITY RESULTS FOR MULTIVALUED SEMILINEAR DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS , 2003 .

[14]  V. Lakshmikantham,et al.  Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space , 1991 .

[15]  L. Byszewski.  Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem , 1991 .

[16]  P. Balasubramaniam.  Existence of solutions of functional stochastic differential inclusions , 2002 .

[17]  B. Dhage,et al.  Multi-valued mappings and fixed points II , 2006 .

[18]  S. Ntouyas.  Existence results for impulsive partial neutral functional differential inclusions. , 2005 .

[19]  A. Pritchard,et al.  Analytic resolvent operators for integral equations in Banach space , 1983 .

[20]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[21]  D. Vinayagam,et al.  Existence of Solutions of Nonlinear Neutral Stochastic Differential Inclusions in a Hilbert Space , 2005 .