Solutions Of K-coupled Schr(?)dinger System And Its Related Equations

In this paper,we mainly study the solutions of k-coupled Schrodinger system and its related equations.Firstly,by constructing an appropriate auxiliary function,the Brezis-Lieb lemma of the single variable is extended to the k-coupled form,and the weak convergence relationship of the vector form is obtained.Secondly.By constructing an appropriate auxiliary problem and applying Zou-Yue's abstract theorem,it is obtained that when the coupling coefficient is a continuous function,the k-system has multiple sign-changing solutions,mixed state of nodal solutions and a positive solution,which generalizes the case where the coupling coefficient are constants.Thirdly,the original SEIR propagation model is improved,that is to say,considering more complex variable coefficients,through the simulation of MATLAB,it is found that the improved model is more realistic.