DOI: 10.1093/imamci/dnag024 ISSN: 0265-0754
Existence and stability of second-order neutral stochastic partial functional differential equations with infinite delay
Yiming Xie, Shengli XieAbstract
The existence and uniqueness of mild solutions for second-order neutral stochastic partial functional differential equations with infinite delay are obtained by utilizing the M$\ddot{o}$nch fixed theorem and the Kuratowski measure of non-compactness. Further, we establish a new Gronwall–Bellman-type integral inequality with infinite delay to prove the exponential stability, asymptotical stability and global attracting set in the $p$th moment of mild solutions. Certain restrictive conditions have been removed. Our results improve and generalize some corresponding results. Finally, an example is given to show our main results.