Solutions of perturbed Schrodinger equations with critical nonlinearity
文献类型：期刊论文
| 作者 | Ding, Yanheng ; Lin, Fanghua
|
| 刊名 | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2007-10-01 |
| 卷号 | 30期号:2页码:231-249 |
| ISSN号 | 0944-2669 |
| DOI | 10.1007/s00526-007-0091-z |
| 英文摘要 | We consider the perturbed Schrodinger equation {(u(x) -> 0) (-epsilon 2 Delta u + V(x)u = P(x)vertical bar u vertical bar p-2u + K(x)vertical bar u vertical bar 2*- 2u) (as vertical bar x vertical bar -> infinity) (for x epsilon RN) where N >= 3, 2* = 2N/(N - 2) is the Sobolev critical exponent, p epsilon (2, 2*), P(x) and K(x) are bounded positive functions. Under proper conditions on V we show that it has at least one positive solution provided that epsilon <= epsilon; for any m epsilon N, it has m pairs of solutions if epsilon <= epsilon(m); and suppose there exists an orthogonal involution tau : R-N -> R-N such that V(x), P(x) and K(x) are tau- invariant, then it has at least one pair of solutions which change sign exactly once provided that epsilon <= epsilon, where epsilon and epsilon(m) are sufficiently small positive numbers. Moreover, these solutions u(epsilon) -> 0 in H-1(R-N) as epsilon -> 0. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000247635600005 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5188]  |
| 专题 | 数学所 |
| 通讯作者 | Lin, Fanghua |
| 作者单位 | 1.NYU, Courant Inst Math Sci, New York, NY 10012 USA 2.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ding, Yanheng,Lin, Fanghua. Solutions of perturbed Schrodinger equations with critical nonlinearity[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,2007,30(2):231-249. |
| APA | Ding, Yanheng,&Lin, Fanghua.(2007).Solutions of perturbed Schrodinger equations with critical nonlinearity.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,30(2),231-249. |
| MLA | Ding, Yanheng,et al."Solutions of perturbed Schrodinger equations with critical nonlinearity".CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 30.2(2007):231-249. |
入库方式： OAI收割
来源：数学与系统科学研究院
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