On the Existence of Solutions for the Critical Fractional Laplacian Equation in RN

We study existence of solutions for the fractional Laplacian equation (-Delta)(s)u + V(x)u = vertical bar u vertical bar(2)*((s)-2)u + f(x, u) in R-N, u is an element of H-s(R-N), with critical exponent 2*(s) = 2N/(N - 2s), N > 2s, s is an element of (0, 1), where V(x) >= 0 has a potential well and f : R-N x R -> R is a lower order perturbation of the critical power vertical bar u vertical bar(2)*((s)-2)u. By employing the variational method, we prove the existence of nontrivial solutions for the equation.