Existence of Normalized Solution for Fractional Nonlinear Schrödinger Systems

本文主要研究了一类分数阶非线性薛定谔系统 在 H s ( R N )× H s ( R N ) 中的规范解的存在性，且解满足 ∫ R N | u 1 | 2 dx = a 1 , ∫ R N | u 2 | 2 dx = a 2 . 其中规定 s∈( 0,1 ), a 1 , a 2 >0, λ 1 , λ 2 ∈R 是以拉格朗日乘子出现的未知参数， h i : R N →[ 0,∞ ) 为有界连续函数。考虑 f i = | u i | p i −2 u i ,i=1,2 且 F( u 1 , u 2 )=ω | u 1 | r 1 | u 2 | r 2 ， ω, r 1 , r 2 是正的常数。This article mainly studies a class of fractional nonlinear Schrödinger coupled systems with the existence of the normalized solution in H s ( R N )× H s ( R N ) , and the solution satisfies ∫ R N | u 1 | 2 dx = a 1 , ∫ R N | u 2 | 2 dx = a 2 . Among them, it is specified that s∈( 0,1 ), a 1 , a 2 >0, λ 1 , λ 2 ∈R is a Lagrange multiplier; h i : R N →[ 0,∞ ) is a bounded continuous function. Consider f i = | u i | p i −2 u i ,i=1,2 and F( u 1 , u 2 )=ω | u 1 | r 1 | u 2 | r 2 , where ω, r 1 , r 2 are positive constant.