We extend the results of Cabre and Sire (2011) to show the existence of layer solutions of fractional Laplacians with perturbed nonlinearity in with . Here is a positive periodic perturbation for , and is the derivative of a balanced well potential . That is, satisfies First, for odd nonlinearity and for every , we prove that there exists a layer solution via the monotone iteration method. Besides, existence results are obtained by variational methods for and for more general nonlinearities. While the case remains open.
Yan Hu. "Existence Results for a Perturbed Problem Involving Fractional Laplacians." Abstr. Appl. Anal. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/548301