In this paper, we study the nonlocal anisotropic −→p (x)-Laplacian problem of the following form − N i=1 Mi Ω |∂xiu|pi(x) pi(x) dx ∂xi |∂xiu|pi(x)−2∂xiu = f(x, u) in Ω, u = 0 on ∂Ω. By means of a direct variational approach and the theory of the anisotropic variable exponent Sobolev space, we obtain the existence and multiplicity of weak energy solutions. Moreover, we get much better results with f in a special form.
