Multiple solutions for a class of nonhomogeneous elliptic systems with Dirichlet boundary or Neumann boundary

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 N and N 1. We exploit the method which is based on 6. This method let us obtain the concrete open interval about the parameter. Since the quasilinear term depends on u and u, it is necessary for our proofs to use the theory of monotone operators and the skill of adding one dimension to space.