  We consider the class of non-linear stochastic partial differential equations
studied in \cite{conusdalang}. Equivalent formulations using integration with
respect to a cylindrical Brownian motion and also the Skorohod integral are
established. It is proved that the random field solution to these equations at
any fixed point $(t,x)\in[0,T]\times \Rd$ is differentiable in the Malliavin
sense. For this, an extension of the integration theory in \cite{conusdalang}
to Hilbert space valued integrands is developed, and commutation formulae of
the Malliavin derivative and stochastic and pathwise integrals are proved. In
the particular case of equations with additive noise, we establish the
existence of density for the law of the solution at $(t,x)\in]0,T]\times\Rd$.
The results apply to the stochastic wave equation in spatial dimension $d\ge
4$.
