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dc.contributor.authorSpradlin, Gregory S. ( )
dc.date.accessioned2021-04-05T20:25:43Z
dc.date.available2021-04-05T20:25:43Z
dc.date.issued2004-02-12
dc.identifier.citationSpradlin, G. S. (2004). Existence of solutions to a Hamiltonian system without convexity condition on the nonlinearity. Electronic Journal of Differential Equations, 2004(21), pp. 1-13.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13340
dc.description.abstractWe study a Hamiltonian system that has a superquadratic potential and is asymptotic to an autonomous system. In particular, we show the existence of a nontrivial solution homoclinic to zero. Many results of this type rely on a convexity condition on the nonlinearity, which makes the problem resemble in some sense the special case of homogeneous (power) nonlinearity. This paper replaces that condition with a different condition, which is automatically satisfied when the autonomous system is radially symmetric. Our proof employs variational and mountain-pass arguments. In some similar results requiring the convexity condition, solutions inhabit a submanifold homeomorphic to the unit sphere in the appropriate Hilbert space of functions. An important part of the proof here is the construction of a similar manifold, using only the mountain-pass geometry of the energy functional.en_US
dc.formatText
dc.format.extent13 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2004, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectMountain Pass Theoremen_US
dc.subjectVariational methodsen_US
dc.subjectNehari manifolden_US
dc.subjectHomoclinic solutionsen_US
dc.titleExistence of solutions to a Hamiltonian system without convexity condition on the nonlinearityen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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