KMS Of Academy of mathematics and systems sciences, CAS
Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents | |
Li, Shujie; Liu, Zhaoli | |
2006-12-01 | |
Source Publication | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS |
ISSN | 1230-3429 |
Volume | 28Issue:2Pages:235-261 |
Abstract | 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. |
Keyword | nonlinear elliptic equation Sobolev exponent multiple solutions |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000242870800002 |
Publisher | JULIUSZ SCHAUDER CTR NONLINEAR STUDIES |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/3456 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Li, Shujie |
Affiliation | 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 |
Recommended Citation 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. |
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