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Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms
Ding, Yanheng
2006-08-01
Source PublicationCOMMUNICATIONS IN CONTEMPORARY MATHEMATICS
ISSN0219-1997
Volume8Issue:4Pages:453-480
AbstractThis paper is concerned with homoclinic orbits in the Hamiltonian system (z) over dot = JH(z) (t, z), where H is periodic in t with H-z (t, z) = L (t) z + R-z (t, z), R-z (t, z) = o(\z\) as z --> 0. We find a condition on the matrix valued function L to describe the spectrum of operator -(Td/dt + L) so that a proper variational formulation is presented. Supposing R-z is asymptotically linear as \z\ --> infinity and symmetric in z, we obtain infinitely many homoclinic orbits. We also treat the case where R-z is super linear as \z\ --> infinity with assumptions different from those studied previously in relative work, and prove existence and multiplicity of homoclinic orbits. Our arguments are based on some recent information on strongly indefinite functionals in critical point theory.
Keywordspectrum infinitely many homoclinics asymptotically linear superlinear critical points
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000240325400002
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/3249
Collection数学所
Corresponding AuthorDing, Yanheng
AffiliationChinese Acad Sci, Inst Math, AMSS, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Ding, Yanheng. Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,2006,8(4):453-480.
APA Ding, Yanheng.(2006).Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms.COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,8(4),453-480.
MLA Ding, Yanheng."Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms".COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 8.4(2006):453-480.
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