We study the existence of infinitely many solutions for anisotropic variable exponent problem of the type − Ni=1 ∂xi (|∂xiu|pi(x)−2∂xiu) + Ni=1 |u|pi(x)−2u = λf (x, u), with the Neumann boundary condition. Here, f is a Carathéodory function and pi are continuous functions on with pi(x) 2. We show the existence of infinitely many solutions for suitable range of λ by analyzing the critical points of the Euler functional. We also study some corollaries of the main results and finally present some examples.
