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ON SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS OF BRIOT–BOUQUET TYPE

Part of: Partial differential equations Representations of solutions

Published online by Cambridge University Press:  29 April 2018

FENGBAI LI Open the ORCID record for FENGBAI LI [Opens in a new window]
FENGBAI LI*
Affiliation:
School of Mathematics, Shanghai University of Finance and Economics, 777 Guo Ding Road, Shanghai, 200433, PR China email li.fengbai@mail.shufe.edu.cn
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Abstract

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We study systems of partial differential equations of Briot–Bouquet type. The existence of holomorphic solutions to such systems largely depends on the eigenvalues of an associated matrix. For the noninteger case, we generalise the well-known result of Gérard and Tahara [‘Holomorphic and singular solutions of nonlinear singular first order partial differential equations’, Publ. Res. Inst. Math. Sci.26 (1990), 979–1000] for Briot–Bouquet type equations to Briot–Bouquet type systems. For the integer case, we introduce a sequence of blow-up like changes of variables and give necessary and sufficient conditions for the existence of holomorphic solutions. We also give some examples to illustrate our results.

Keywords

partial differential equations of Briot–Bouquet typeholomorphic solutionsblow-upchange of variables

MSC classification

Primary: 35A20: Analytic methods, singularities
Secondary: 35C10: Series solutions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 122 - 133
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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