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dc.contributor.authorXie, Xuming ( )
dc.date.accessioned2020-10-05T18:49:06Z
dc.date.available2020-10-05T18:49:06Z
dc.date.issued2003-03-28
dc.identifier.citationXie, X. (2003). Analytic solution to a class of integro-differential equations. Electronic Journal of Differential Equations, 2003(33), pp. 1-25.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12705
dc.description.abstract

In this paper we consider the integro-differential equation

2y''(x) + L(x) H(y) = N(∈, x, y, H(y)),

where H(y) [x] = 1/π(P) ∫-∞ y(t)/t-x dt is the Hilbert transform. The existence and uniqueness of analytic solution in appropriately chosen space is proved. Our method consists of extending the equation to an appropriately chosen region in the complex plane, then use the Contraction Mapping Theorem.

en_US
dc.formatText
dc.format.extent25 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, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectAnalytic solutionen_US
dc.subjectSingular integro-differential equationen_US
dc.titleAnalytic solution to a class of integro-differential equationsen_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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