  We are interested in looking for two nontrivial solutions for a class of
nonhomogeneous quasilinear elliptic system with sign-changing weight functions
and concave-convex nonlinearities on the bounded domain. This kind of
quasilinear elliptic system arises from nonlinear optics, whose feature is that
its differential operator depends on not only $\nabla u$ but also $u$.
Employing the mountain pass theorem and Ekeland's variational principle as the
major tools, we show that the system has at least one nontrivial solution of
positive energy and one nontrivial solution of negative energy, respectively.
