We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential crit...We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.展开更多
本文在Sobolev-Lorentz空间W^(2)L^(2,q)(R^(4))的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp MoserTrud...本文在Sobolev-Lorentz空间W^(2)L^(2,q)(R^(4))的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp MoserTrudinger and Adams type inequalities:a rearrangement-free argument,J.Diff Equ.,2013,255(3):298-325]的分割水平集方法.展开更多
基金Natural Science Foundation of China(Grant Nos.11601190 and 11661006)Natural Science Foundation of Jiangsu Province(Grant No.BK20160483)Jiangsu University Foundation Grant(Grant No.16JDG043)。
文摘We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.
文摘本文在Sobolev-Lorentz空间W^(2)L^(2,q)(R^(4))的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp MoserTrudinger and Adams type inequalities:a rearrangement-free argument,J.Diff Equ.,2013,255(3):298-325]的分割水平集方法.
