  We study a degenerate elliptic system with variable exponents. Using the
variational approach and some recent theory on weighted Lebesgue and Sobolev
spaces with variable exponents, we prove the existence of at least two distinct
nontrivial weak solutions of the system. Several consequences of the main
theorem are derived; in particular, the existence of at lease two distinct
nontrivial nonnegative solution are established for a scalar degenerate
problem. One example is provided to showthe applicability of our results.
