Concentration Behavior Of Solutions For Coupled Fractional Nonlinear Schr(?)dinger Equations

In the past ten years,due to the important applications in nonlinear optics,BoseEinstein condensation and other physical problems,nonlinear Schrodinger equations have received widespread attention.Many scholars have done a lot of outstanding research work on nonlinear Schrodinger equations.In this article,we mainly explore the existence of the solutions of the following fractional Schrodinger system and the concentration of solutions when ε→0.Where,(—Δ)s is the fractional Laplace operator,0<s<1,μ1,μ2>0,1<p<min{3,(2N/N-2s)-1},β<0;We assume that the potential function Vi(x)(i=1,2)satisfies the following two conditions:(1)Vi∈C∞(RN),Vi(x)≥ai>0,x∈ RN;(2)(?)M>0,meas {x∈RN | Vi(x)<M}<∞.In the third chapter of this article,we use the constraint minimization method and the Lagrange multiplier method to prove that when(?)(?)and potential function Vi(x)(i=1,2)satisfies the above two conditions,the system has ground state solution.In the forth chapter,we discusses the concentration behavior of the ground state solution when ε→0.First,we establish the decomposition lemma(Lemma4.1),and then compare the energy of the coupling equation and the limit equation(Lemma 4.2),finally based on Lemma 4.1 and Lemma 4.2,we prove that whenε→0,the ground state solution concentrates to the unique global minimum point of the potential function.