  In this paper, we study the Dirichlet problem for the implicit degen- erate
nonlinear elliptic equation with variable exponent in a bounded domain. We
obtain sufficient conditions for the existence of a solution with- out
regularization and any restriction between the exponents. Furthermore, we
define the domain of the operator generated by posed problem and investigate
its some properties and also its relations with known spaces that enable us to
prove existence theorem.
