  We extend some methods developed by Albeverio, Brze\'{z}niak and Wu and we
show how to apply them in order to prove existence of global strong solutions
of stochastic differential equations with jumps, under a local one-sided
Lipschitz condition on the drift (also known as a monotonicity condition) and a
local Lipschitz condition on the diffusion and jump coefficients, while an
additional global one-sided linear growth assumption is satisfied. Then we use
these methods to prove existence of invariant measures for a broad class of
such equations.
