This paper aims to investigate the existence of distributional solutions in ˚W 1,−→p (・)(Ω) (i.e. the anisotropic Sobolev space with variable exponents and zero boundary) for a class of nonlinear anisotropic elliptic equations with variable exponents and a lower-order term that has natural growth with respect to |∂iu|, i = 1, . . . ,N. The datum f on the right-hand side belongs to the space L(p∗)′(・)(Ω), where Ω ⊂ RN (N ≥ 2) is a bounded open Lipschitz domain and (p∗)′(・) represents the H¨older conjugate of the Sobolev conjugate p(・).
