We use the variational approach to investigate periodic measures for a class of stochastic partial differential equations (SPDEs) with regime-switching. The hybrid system is driven by degenerate Lévy noise. We use the Lyapunov function method to study the existence of periodic measures and show the uniqueness of periodic measures by establishing the strong Feller property and irreducibility of the associated time-inhomogeneous semigroup. The main results are applied to stochastic fractional porous medium equations with regime-switching.

中文翻译：

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具有状态切换的一类 SPDE 的定期测量

我们使用变分方法来研究一类具有状态切换的随机偏微分方程 (SPDE) 的周期测量。混合系统由简并 Lévy 噪声驱动。我们使用Lyapunov函数方法来研究周期测度的存在性，并通过建立相关的时间非齐次半群的强Feller性质和不可约性来证明周期测度的唯一性。主要结果应用于具有状态切换的随机分数多孔介质方程。