Existence of Semiclassical States for a Quasilinear Schr?dinger Equation on R^N with Exponential Critical Growth

作     者：Shao Jun LI Carlos A. SANTOS Min Bo YANG 

作者机构：Department of MathematicsZhejiang Normal UniversityJinhua 321004P.R.China Universidade de BrasiliaDepartamento de Matematica70910-900 BrasiliaDFBrazil 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2016年第32卷第11期

页      面：1279-1296页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：partially supported by PROCAD/UFG/Un B and FAPDF(Grant No.PRONEX 193.000.580/2009) partially supported by NSFC(Grant Nos.11571317,11101374,11271331) ZJNSF(Grant No.Y15A010026) 

主　　题：Exponential critical growth semiclassical solutions variational methods 

摘      要：We study a quasilinear Schrodinger equation {-εN△Nu＋V（x）｜u｜N-2= Q（x）f（u） in R^N,0〈u∈W1,N（RN）,u（x）^｜x｜→∞0,where V, Q are two continuous real functions on R^N and c 〉 0 is a real parameter. Assume that the nonlinearity f is of exponential critical growth in the sense of Trudinger-Moser inequality, we are able to establish the existence and concentration of the semiclassical solutions by variational methods. Keywords Exponential critical growth, semiclassical solutions, variational methods