Existence Of L~2-constrained Solutions Of A Class Schr(?)dinger Systems

The nonlinear schr(?)dinger equation is a class of nonlinear equations containing isolated on wave solutions.It is closely related to many nonlinear problems in theoretical physics such as nonlinear optics,ionic acoustic waves of plasma,etc.Therefore,the study of the solutions of nonlinear schr(?)dinger equations has been favored by many scientists.In recent years,relevant scholars have made very fruitful results in the existence and multiplicity of equation solutions.This paper mainly studies the existence and multiplicity of nonlinear schr(?)dinger equation and L2 constraint solutions of systems.Under the new Palais-Smale condition,Studying the new deformation parameters on the restricted functional Sm={u:∫RN|u|2dx=m} and Sm1×Sm2,Applying the maxima minor theory and other topological tools to obtain results on the nonlinear schr(?)dinger equation and system existence and multiplicity.