Stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity and delay

Abstract

In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results.

Keywords:

• Stochastic partial functional differential equation
• local monotonicity
• local Lipschitz condition

AMS Subject Classifications:

• 35K20
• 60H15
• 60H40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was supported in part by NSFC of China [grant number 11301146], [grant number 11171064]. The second author was supported in part by NUS AcRF [grant number R-146-000-213-112].