Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents
文献类型：期刊论文
| 作者 | Li, Shujie; Liu, Zhaoli |
| 刊名 | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
 |
| 出版日期 | 2006-12-01 |
| 卷号 | 28期号:2页码:235-261 |
| 关键词 | nonlinear elliptic equation Sobolev exponent multiple solutions |
| ISSN号 | 1230-3429 |
| 英文摘要 | We study multiplicity of solutions of the following elliptic problems in which critical and supercritical Sobolev exponents are involved: -Delta u = g(x, u) + lambda h(x, u) in Omega and u = 0 on partial derivative Omega, -div(\del u\(p-2)del u) = g(x, u) + lambda h(x, u) in Omega and u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-N, p > 1, lambda is a parameter, and lambda h(x, u) is regarded as a perturbation term of the problems. Except oddness with respect to u in some cases, we do not assume any condition on h. For the first problem, we get a result on existence of three nontrivial solutions for \lambda\ small in the case where g is superlinear and lim sup(\t\-->infinity) g(x, t)/\t\(2*-1) is suitably small. We also prove that the first problem has 2k distinct solutions for \lambda\ small when g and h are odd and there are k eigenvalues between lim(t-->0) g(x, t)/t and lim(\t\-->infinity) g(x, t)/t. For the second problem, we prove that it has more and more distinct solutions as lambda tends to 0 assurning that g and h are odd and g is superlinear and lim(\t\-->infinity) g(x, t,)/\t\(p*-1) = 0. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000242870800002 |
| 出版者 | JULIUSZ SCHAUDER CTR NONLINEAR STUDIES |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3455]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Li, Shujie |
| 作者单位 | 1.Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Harbin Normal Univ, Yuan Rong Zeng Funct Anal Res Ctr, Harbin 150025, Peoples R China 3.Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Shujie,Liu, Zhaoli. Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents[J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,2006,28(2):235-261. |
| APA | Li, Shujie,&Liu, Zhaoli.(2006).Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents.TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS,28(2),235-261. |
| MLA | Li, Shujie,et al."Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents".TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS 28.2(2006):235-261. |
入库方式： OAI收割
来源：数学与系统科学研究院
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