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Multiplicity of solutions for some elliptic equations involving critical and supercritical Sobolev exponents
Li, Shujie; Liu, Zhaoli
2006-12-01
Source PublicationTOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
ISSN1230-3429
Volume28Issue:2Pages:235-261
AbstractWe 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.
Keywordnonlinear elliptic equation Sobolev exponent multiple solutions
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000242870800002
PublisherJULIUSZ SCHAUDER CTR NONLINEAR STUDIES
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/3456
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLi, Shujie
Affiliation1.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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