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Zbl 1189.60119
Lin, Aihong; Hu, Lanying
Existence results for impulsive neutral stochastic functional integro-differential inclusions with nonlocal initial conditions. (English)
[J] Comput. Math. Appl. 59, No. 1, 64-73 (2010). ISSN 0898-1221

Summary: 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.

MSC 2000:: *60H10 Stochastic ordinary differential equations
34G20 Nonlinear ODE in abstract spaces
45R05 Random integral equations

Keywords: impulsive equation; neutral equation; stochastic functional integro-differential inclusion; resolvent operator; mild solution; nonlocal initial condition

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Zentralblatt MATH Berlin [Germany]