Show simple item record

dc.contributor.authorBattelli, Flaviano ( Orcid Icon 0000-0001-9650-6847 )
dc.contributor.authorFeckan, Michal ( )
dc.date.accessioned2020-07-13T20:35:30Z
dc.date.available2020-07-13T20:35:30Z
dc.date.issued2002-02-07
dc.identifier.citationBattelli, F., & Feckan, M. (2002). Some remarks on the Melnikov function. Electronic Journal of Differential Equations, 2002(13), pp. 1-29.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12053
dc.description.abstractWe study the Melnikov function associated with a periodic perturbation of a differential equation having a homoclinic orbit. Our main interest is the characterization of perturbations that give rise to vanishing or non-vanishing of the Melnikov function. For this purpose we show that, in some cases, the Fourier coefficients of the Melkinov function can be evaluated by means of the calculus of residues. We apply this result, among other things, to the construction of a second-order equation whose Melnikov function vanishes identically for any C1, 2π-periodic perturbation. Then we study the second order Melnikov function of the perturbed equation, and prove it is non-vanishing for a large class of perturbations.en_US
dc.formatText
dc.format.extent29 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectMelnikov functionen_US
dc.subjectResiduesen_US
dc.subjectFourier coefficientsen_US
dc.titleSome Remarks on the Melnikov Functionen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record