文献类型：期刊文献

英文题名：A monotone property of the ground state energy to the scalar field equation and applications

作者：Ji, Chao[1];Wang, Zhi-Qiang[2,3];Wu, Yuanze[4]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Fujian, Peoples R China;[3]Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA;[4]China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China

年份：2019

卷号：100

期号：3

起止页码：804

外文期刊名：JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000501379600005)】；

语种：英文

外文关键词：35J20; 35B25; 35B38; 35B40 (primary)

摘要：We consider the ground state energy m(p,lambda) for the classical nonlinear scalar field equation-Delta u+lambda u=|u|p-2u,x is an element of RN,where N > 3, lambda>0, 2ep-2p2N-(N-2)p2p is fixed. For applications, we establish the existence and the concentration behavior of the least energy solutions (positive or sign changing) for the singularly perturbed elliptic equation with a variable exponent p(x):-epsilon 2 Delta u+lambda u=|u|p(x)-2u,u is an element of H1(RN).Our results show that the concentration behavior of the least energy solutions of the above equation is quite different from that of the semi-classical states of nonlinear Schrodinger equations with p being a constant: -epsilon 2 Delta u+V(x)u=|u|p-2u. Roughly speaking, for small lambda, the least energy solution concentrates at the global minimum point of p(x), and for large lambda, the least energy solution concentrates at the global maximum point of p(x). This is a striking new phenomenon which, to the best of our knowledge, has not been studied before.