Normalized Solutions Of Nonlinear Schrodinger Equations In R~2 Involving Exponential Nonlinearities

Schrodinger equation is a basic model in quantum mechanics,which plays an important role in Bose Einstein condensation and other problems.This paper is devoted to using a variational method to find the existence of normalized solutions of the following Schrodinger equation where the normalized condition p>0 is given and the Lagrange number λ∈R is un-known.By combing with the Ekeland variational principle,Trudinger-Moser inequality and Nehari-Pohozaev identical equation,we get the existence of normalized solutions when the exponential nonlinearities are involved.