Abstract
This paper is concerned with the existence and asymptotic behavior of mild solutions to a class of non-linear neutral stochastic partial differential equations with infinite delays. By applying fixed point principle, we present sufficient conditions to ensure that the mild solutions are exponentially stable in $p$th-moment ($p\geq 2$) and almost surely exponentially stable. An example is provided to illustrate the effectiveness of the proposed result.
Highlights
In recent years, there has been considerable interest in studying the quantitative and qualitative properties of solutions to stochastic partial differential equations (SPDEs) in a separable Hilbert space such as existence, uniqueness, stability, controllability and asymptotic behavior
This paper is concerned with the existence and asymptotic behavior of mild solutions to a class of non-linear neutral stochastic partial differential equations with infinite delays
By applying fixed point principle, we present sufficient conditions to ensure that the mild solutions are exponentially stable in pth-moment (p ≥ 2) and almost surely exponentially stable
Summary
There has been considerable interest in studying the quantitative and qualitative properties of solutions to stochastic partial differential equations (SPDEs) in a separable Hilbert space such as existence, uniqueness, stability, controllability and asymptotic behavior (see, e.g., [1, 6, 17, 18, 21, 22, 23, 24, 25] and references therein). Asymptotic behavior for NSPDEs with infinite delays investigation on the stability of mild solutions to neutral SPDEs with delays. In this paper, motivated by the previous references, we are concerned with the existence and asymptotic behavior of mild solutions to a class of neutral SPDEs with infinite delays. An example is provided to illustrate the effectiveness of the proposed result
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