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Semilinear stochastic evolution equations with L\'evy noise and monotonenonlinear drift are considered. The existence and uniqueness of the mildsolutions in $L^p$ for these equations is proved and a sufficient condition forexponential asymptotic stability of the solutions is derived. The main tool inour study is an It\^o type inequality for the $p$th power of stochasticconvolution integrals in Hilbert spaces.

Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$