Existence Of Non-negative Solutions For A Class Of Nonlinear Elliptic Equations With Singular Trudinger-moser Terms

We consider the existence of nonnegative solutions of the Dirichlet problem with singular Trudinger-Moser term,Let ? be a bounded domain in R2 containing the origin,where u = u(x),f(u)=g(u)ebu2is the critical growth function,the critical exponent is b/4?+?/2= 1.Through the study of the singular Trudinger-Moser embedding and the mountain pass lemma,we shall prove the existence of non-negative solutions of the above nonlinear elliptic equations...