Abstract In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDEs, where the coefficients satisfy a specific type Lyapunov condition instead of the classical coercivity condition. Moreover, based on the generalized variational framework, we also use the local monotonicity condition to replace the standard monotonicity condition, which is applicable to various quasilinear and semilinear BSPDE models.

中文翻译：

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具有李雅普诺夫条件的后向随机偏微分方程的适定性

摘要 在本文中，我们展示了一大类反向 SPDE 的强解的存在性和唯一性，其中系数满足特定类型的李雅普诺夫条件而不是经典矫顽力条件。此外，基于广义变分框架，我们还使用局部单调性条件代替标准单调性条件，适用于各种拟线性和半线性BSPDE模型。