On entire solutions of a family of nonlinear partial differential equations of prime degree

We characterize entire solutions of a new family of nonlinear first-order partial differential equations of prime degree p (equation 1 ). In particular, we show that in the Borel family (defined in the article) of entire functions in the entire solutions of ( 1 ) are of exponential form. Then, we ad...

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Bibliographic Details
Published inComplex variables and elliptic equations Vol. 52; no. 4; pp. 287 - 298
Main Author Saleeby, Elias G.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.04.2007
Subjects
AMS 2000 Mathematics Subject Classifications: 35F20
Entire solutions
Exponential functions
Nonlinear partial differential equations
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Summary:We characterize entire solutions of a new family of nonlinear first-order partial differential equations of prime degree p (equation 1 ). In particular, we show that in the Borel family (defined in the article) of entire functions in the entire solutions of ( 1 ) are of exponential form. Then, we address the general case when p =  3 , and show that under some natural conditions the entire solutions are also of exponential form.
ISSN:1747-6933
1747-6941
DOI:10.1080/17476930600842220