Multiplicity of solutions for a class of superlinear non-local fractional equations

In this paper, we are concerned with the problem driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions. As a particular case, we study multiple solutions for the following non-local fractional Laplace equations:where is fixed parameter, is an open bounded subset of with smooth boundary () and is the fractional Laplace operator. By a variant version of the Mountain Pass Theorem, a multiplicity result is obtained for the above-mentioned superlinear problem without Ambrosetti-Rabinowitz condition. Consequently, the result may be looked as a complete extension of the previous work of Wang and Tang to the non-local fractional setting.