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Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential,…) Equations

FASdiff 2017: Formal and Analytic Solutions of Diff. Equations pp 47–59Cite as

Singular Solutions to a System of Equations related to Ricci-Flat Kähler Metrics

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 256))

Abstract

In the 1990s, Gérard and Tahara studied a class of singular partial differential equations and proved that such equations admit both holomorphic and singular solutions. Using an asymptotic approach, they showed that the obtained singular solution is unique in some space. In this paper, we will establish the existence of singular solutions to a system of partial differential equations considered by Bielawski. We then employ the asymptotic approach of Gérard and Tahara to prove its uniqueness in some space.

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References

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Acknowledgements

The authors acknowledge the Office of the Chancellor of the University of the Philippines Diliman, through the Office of the Vice Chancellor for Research and Development, for funding support through the Outright Research Grant.

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Authors and Affiliations

  1. Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines

    Jose Ernie C. Lope

  2. Institute of Mathematics, University of the Philippines, Diliman Quezon City, Philippines

    Mark Philip F. Ona

Authors
  1. Jose Ernie C. Lope
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  2. Mark Philip F. Ona
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Corresponding author

Correspondence to Jose Ernie C. Lope .

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Editors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  2. Departamento de Física y Matemáticas, University of Alcalá, Alcalá de Henares, Spain

    Alberto Lastra

  3. Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

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Lope, J.E.C., Ona, M.P.F. (2018). Singular Solutions to a System of Equations related to Ricci-Flat Kähler Metrics. In: Filipuk, G., Lastra, A., Michalik, S. (eds) Formal and Analytic Solutions of Diff. Equations . FASdiff 2017. Springer Proceedings in Mathematics & Statistics, vol 256. Springer, Cham. https://doi.org/10.1007/978-3-319-99148-1_3

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