  In this paper, we mainly establish the existence of at least three
non-trivial solutions for a class of nonhomogeneous quasilinear elliptic
systems with Dirichlet boundary value or Neumann boundary value in a bounded
domain $\Omega\subset\mathbb{R}^N $ and $N\geq 1$. We exploit the method which
is based on [6]. This method let us obtain the concrete open interval about the
parameter $\lambda$. Since the quasilinear term depends on $u$ and $\nabla u$,
it is necessary for our proofs to use the theory of monotone operators and the
skill of adding one dimension to space.
