  In this paper we consider quasilinear elliptic equations driven by the
variable exponent double phase operator with superlinear right-hand sides.
Under very general assumptions on the nonlinearity, we prove a multiplicity
result for such problems whereby we show the existence of a positive solution,
a negative one and a solution with changing sign. The sign-changing solution is
obtained via the Nehari manifold approach and, in addition, we can also give
information on its nodal domains.
