In this article, we study the nonlocal p(x)-Laplacian problem of the following form where Ω is a smooth bounded domain and ν is the outward normal vector on the boundary ∂Ω, and . By using the variational method and the theory of the variable exponent Sobolev space, under appropriate assumptions on f, g, a and b, we obtain some results on existence and multiplicity of solutions of the problem. Mathematics Subject Classification (2000): 35B38; 35D05; 35J20.
