Existence And Concentration Of Ground State Solutions For Chern-Simons-Schr(?)dinger Systems With Steep Well Potential

In this paper,we investigate the following Chern-Simons-Schr(?)dinger system(?)where(?),(?),x=(x1,x2)?R2,Aj:R2?R,j=0,1,2 is the gauge field,V?(x)=?V(x)+1,A>0,.f is the nonlinearity.We investigate the existence and concentration behaviour of ground state solutions of the system(0.0.2)in the Chapter 2,3.Firstly,in Chapter 2,we research the existence and concentration of ground state solutions for the system(0.0.2)in H1(R2)with f(u)=|u|p-2u,p>4.By using the variational methods,mountain pass lemma and the Nehari manifold methods,we obtain the existence of ground state solutions of the system when A>0 is large enough.Furthermore,we study the convergence property of ground state solutions as ??+?.Then,in Chapter 3,we extend f to the case of general 5-superlinear growth.We study the existence of ground state solutions for the system(0.0.2)and the con-centration behaviour of solutions as ??+?.Based on the variational methods and the mountain pass lemma,we get the existence of nontrivial solutions of the system.Moreover,by using the definition of ground state solution,we prove the existence of ground state solutions.