Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction

Abstract

In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region principle) and prove the symmetry and nonexistence of positive solution of this nonlocal system. Second, we make complete classification of positive solutions of the system in the critical case when some parameters are equal. Finally, we prove the existence of multiple nontrivial solutions in the critical case according to the different parameters ranges by using variational methods. To accomplish our results we establish the maximum principle for the fractional nonlocal system.

Keywords

• fractional laplacians
• nonlinear fractional hartree system
• variational methods
• 35j61
• 35j20
• 35q55
• 49j40