Electronic Journal of Differential Equations (Sep 2017)
Multiple solutions of nonlinear fractional elliptic equations via Morse theory
Abstract
This article concerns the existence and multiplicity of weak solutions of the nonlinear fractional elliptic problem. We extend some well known results of semilinear Laplacian equations to the nonlocal fractional setting. Using the variational methods based on the critical point theory, sub-supersolutions methods and Morse theory, we show that the problem has at least 6 nontrivial solutions.