Ground state solutions for a class of gauged Schrodinger equations with subcritical and critical exponential growth

摘要

We study a class of gauged nonlinear Schrodinger equations-Delta u+omega u+lambda integral|x|infinity h(s)su2(s)ds+h2(|x|)|x|2)u=f(u)inR2,u is an element of Hr1(R2),where omega,lambda>0 andh(s)=integral 0sr2u2(r)dr.Under some suitable assumptions on f with critical exponential growth, we obtain a positive ground state solution by the non-Nehari manifold method. When f(u) has subcritical exponential growth, we prove the existence of a positive ground state solution by using a new approach. Our results generalize and improve the ones in Ji-Fang [J. Math. Anal. Appl. 450 (2017) 578-591], Byeon et al [J. Funct. Anal. 263 (2012) 1575-1608], and some other related literatures.