  Semilinear stochastic evolution equations with multiplicative L\'evy noise
and monotone nonlinear drift are considered. Unlike other similar work we do
not impose coercivity conditions on coefficients. Existence and uniqueness of
the mild solution is proved using an iterative method. The continuity of the
solution with respect to initial conditions and coefficients is proved and a
sufficient condition for exponential asymptotic stability of the solutions has
been derived. The solutions are proved to have a Markov property. Examples on
stochastic partial differential equations and stochastic delay equations are
provided to demonstrate the theory developed. The main tool in our study is an
It\^o type inequality which gives a pathwise bound for the norm of stochastic
convolution integrals.
