Asymptotic behavior for neutral stochastic partial differential equations with infinite delays

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.