Minimization and error estimates for a class of the nonlinear Schrodinger eigenvalue problems

摘要

It is shown that the nonlinear eigenvaiue problem can be transformed into a constrained functional problem. The corresponding minimal function is a weak solution of this nonlinear problem. In this paper, one type of the energy functional for a class of the nonlinear SchrSdinger eigenvalue problems is proposed, the existence of the minimizing solution is proved and the error estimate is given out.