The Existence Of Ground State Solutions For Asymptotically Periodic Linearly Couple Schr?dinger Equations With Critical Exponent

With the continuous exploration of experts and scholars,the application area of the Schrodinger equation has been expanded,the research methods are constantly updated.When classical variational calculus combines with topology,the formation of a wide range of variational calculus and the theory of critical point for us to solve the problem of the nonlinear equation of the many similar to Schrodinger equation provides a new train of thought,the classical variational law as having a lower or upper functional extremum problem provides a research method,Nehari manifold method in critical point theory as well as we found that the structure of the energy-functional extreme value point provides the skills.In this paper,the classical variational method and Nehari manifold method are combined to transform the solution process of asymptotically periodic linear coupled Schrodinger system equation with critical exponent into the minimum point problem of finding the minimum value of the corresponding energy functional and finally finding the ground state solution of the equation.