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Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces


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1 Department of Mathematics, SRMV College of Arts and Science, Coimbatore-641 020, Tamilnadu, India
     

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In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.

Keywords

Approximate Controllability, Fixed Point Theorems, Stochastic Differential Equation, Mild Solution.
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  • Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces

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Authors

R. Nirmalkumar
Department of Mathematics, SRMV College of Arts and Science, Coimbatore-641 020, Tamilnadu, India
R. Murugesu
Department of Mathematics, SRMV College of Arts and Science, Coimbatore-641 020, Tamilnadu, India

Abstract


In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.

Keywords


Approximate Controllability, Fixed Point Theorems, Stochastic Differential Equation, Mild Solution.

References