Existence Of Solutions For A Class Of Chern-Simons-Schr(?)dinger Systems

The Chern-Simons-Schr(?)dinger system has been a hot research topic for sci-entists since it was proposed.In recent years,significant progress has been made in related research,and high-temperature superconductors,Aharonov-Bohm scat-tering,and the quantum Hall e(?)ect have been widely applied.Therefore,relevan-t scholars have been exploring the existence and multiplicity of solutions for the Chern-Simons-Schr(?)dinger system,as well as other properties,and have achieved rich results.In this paper,we mainly study the existence and concentration of solutions for a class of Chern-Simons-Schr(?)dinger systems with an external potential.We main-ly construct the energy functional of the nonlocal semilinear Schrodinger equation with a gauge field and a non-constant external potential,use the variational method and critical point theory to find the(C)_csequence near the Pohozaev epidemic,and discuss its boundedness and compactness,thereby obtaining the existence and con-centration of nontrivial solutions to the nonlocal semilinear Schrodinger equation.