Variational methods for Nonlinear fractional systems

The main objective of this work is to study the concept of existence and multiplicity of nontrivial solutions for several classes of fractional nonlinear Schrӧdinger-Poisson systems and fractional nonlinear Kirchhoff-Schrӧdinger-Poisson systems, driven by two types of fractional operators in suitable fractional frameworks. More precisely, we analyze different classes of these fractional nonlinear systems under different types of assumptions imposed on the potential functions and nonlinearities. To establish these results, we mainly use variational methods based on the mountain pass theorem, Ekeland variational principles, the fountain theorem and the dual fountain theorem.