This paper is devoted to studying the existence of distributional solutions
for a boundary value problems associated to a class of anisotropic nonlinear
elliptic equations with variable exponents characterized by two strictly
positive? ?W1, ??p(?)(?) first order terms (the weight functions belong to
the anisotropic variable exponents Sobolev space with zero boundary), and
this is in bounded open Lipschitz domain (with Lipschitz boundary) of RN (N
? 2). The functional setting involves anisotropic varible exponents
Lebesgue-Sobolev spaces.