Standing waves with a critical frequency for a quasilinear Schrodinger equation
发布时间：2020-09-30
点击次数：
- 论文类型：
- 期刊论文
- 发表时间：
- 2020-12-01
- 发表刊物：
- COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
- 收录刊物：
- SCIE
- 文献类型：
- J
- 卷号：
- 22
- 期号：
- 8
- ISSN号：
- 0219-1997
- 关键字：
- Quasilinear Schrodinger equation; positive solution; critical frequency
- 摘要：
- We consider the following quasilinear Schrodinger equation
-epsilon(2)Delta omega + V(x)omega - epsilon(2)Delta(omega(2))omega = h(omega), omega > 0, x is an element of R-N.
where N >= 4, lim V(x) > inf(vertical bar x vertical bar)(->infinity) V(x) > inf(x is an element of RN) V(x) = 0, and h satisfies a weaker growth condition than the Ambrosetti-Rabinowitz type condition in Byeon and Wang [Standing waves with a critical frequency for nonlinear Schrodinger equations, Arch. Ration. Mech. Anal. 165(4) (2002) 295-316; Standing waves with a critical frequency for nonlinear Schrodinger equations, II, Calc. Var. 18(2) (2003) 207-219]. We obtain the existence of the localized bound state solutions concentrating at an isolated component of the local minimum of V and whose amplitude goes to 0 as epsilon -> 0.
- 第一作者
- Fang, Xiang-Dong
- 通讯作者
- Fang, XD (corresponding author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.