Semilinear elliptic equations for the fractional Laplacian involving critical exponential growth

We establish the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional Laplacian operator, nonlinearities with critical exponential growth, and potentials that may change sign. The proofs of our existence results rely on minimization methods and the mountain pass theorem. Copyright (C) 2016 John Wiley & Sons, Ltd.