Show simple item record

dc.contributor.authorCecchi, Mariella ( )
dc.contributor.authorFuri, Massimo ( )
dc.contributor.authorMarini, Mauro ( )
dc.contributor.authorPera, Maria Patrizia ( Orcid Icon https://orcid.org/0000-0003-2667-8875 )
dc.date.accessioned2019-09-24T14:54:26Z
dc.date.available2019-09-24T14:54:26Z
dc.date.issued1999-10-31
dc.identifier.citationCecchi, M., Furi, M., Marini, M., & Pera, M. P. (1999). Fredholm linear operators associated with ordinary differential equations on noncompact intervals. Electronic Journal of Differential Equations, 1999(44), pp. 1-16.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/8648
dc.description.abstractIn the noncompact interval J = [α, ∞) we consider a linear problem of the form Lx = y, x ∈ S, where L is a first order differential operator, y a locally summable function in J, and S a subspace of the Fréchet space of the locally absolutely continuous functions in J. In the general case, the restriction of L to S is not a Fredholm operator. However, we show that, under suitable assumptions, S and L(S) can be regarded as subspaces of two quite natural spaces in such a way that L becomes a Fredholm operator between them. Then, the solvability of the problem will be reduced to the task of finding linear functionals defined in a convenient subspace of L1(loc) (J, Rn) whose “kernel intersection” coincides with L(S). We will prove that, for a large class of “boundary sets” S, such functionals can be obtained by reducing the analysis to the case when the function y has compact support. Moreover, by adding a suitable stronger topological assumption on S, the functionals can be represented in an integral form. Some examples illustrating our results are given as well.en_US
dc.formatText
dc.format.extent16 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, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectFredholm operatorsen_US
dc.subjectNoncompact intervalsen_US
dc.titleFredholm Linear Operators Associated with Ordinary Differential Equations on Noncompact Intervalsen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons Attribution 4.0 International License https://creativecommons.org/licenses/by/4.0/


Download

Thumbnail

This item appears in the following Collection(s)

Show simple item record