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In this paper, we study the explosive solutions to a class of parbolic stochastic semilinear differential equations driven by a Lévy type noise. The sufficient conditions are presented to guarantee the existence of a unique positive solution of the stochastic partial differential equation under investigation. Moreover, we show that positive solutions will blow up in finite time in mean *L ^{p}*-norm sense, provided that the initial data, the nonlinear term and the multiplicative noise satisfies some conditions. Several examples are presented to illustrate the theory. Finally, we establish a global existence theorem based on a Lyapunov functional and prove that a stochastic Allen-Cahn equation driven by Lévy noise has a global solution.

In this paper, we investigative the large time decay and stability to any given global smooth solutions of the 3D incompressible inhomogeneous MHD systems. We prove that given a solution $(a, u, B)$ of (2), the velocity field and the magnetic field decay to zero with an explicit rate, for $u$ which coincide with incompressible inhomogeneous Navier-Stokes equations ^{[1]}. In particular, we give the decay rate of higher order derivatives of $u$ and $B$ which are useful to prove our main stability result. For a large solution of (2) denoted by $(a, u, B)$, we show that a small perturbation of the initial data still generates a unique global smooth solution and the smooth solution keeps close to the reference solution $(a, u, B)$. At last, we should mention that the main results in this paper are concerned with large solutions.

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