The Existence Of Solutions For Fractional Nonlinear Schr(?)dinger Systems

In this paper,we study the existence and stability of standing waves for nonlinear fractional Schr(?)dinger equations with three wave interaction in different cases:The paper has three chapters:The first chapter gives the background and main results of the Schr(?)dinger equations(system),the main work of this paper and the required preliminary knowledge.In the second chapter,we consider the nonlinear fractional Schr(?)dinger equations with three-wave interaction.When2 < p < 1 +(4?)/N,the existence and stability of standing waves by using the variational method,the compactness principle and the commutator estimates.In the third chapter,when 2 < p <(N +2?)/(N-2?),we use the Nehari manifold method and the critical point theory to discuss the existence of solutions under constant potential and very potential potential,respectively.