  Semilinear stochastic evolution equations with multiplicative L\'evy noise
and monotone nonlinear drift are considered. Unlike other similar works, we do
not impose coercivity conditions on coefficients. We establish the continuous
dependence of the mild solution with respect to initial conditions and also on
coefficients which as far as we know, has not been proved before. As
corollaries of the continuity result, we derive sufficient conditions for
asymptotic stability of the solutions, we show that Yosida approximations
converge to the solution and we prove that solutions have Markov property.
Examples on stochastic partial differential equations and stochastic delay
differential equations are provided to demonstrate the theory developed. The
main tool in our study is an inequality which gives a pathwise bound for the
norm of stochastic convolution integrals.
