Existence of three solutions for a class of fractional boundary value systems

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We also give an example to illustrate the obtained result.