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Article: On admissible entire solutions of Pell type functional equation f2 + ag2 = 1
| Title | On admissible entire solutions of Pell type functional equation f2 + ag2 = 1 |
|---|---|
| Authors | |
| Keywords | Entire admissible solutions Non-linear differential equation Pell type functional equations |
| Issue Date | 2019 |
| Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmaa |
| Citation | Journal of Mathematical Analysis and Applications, 2019, v. 480 n. 1, p. article no. 123240 How to Cite? |
| Abstract | Given a non-zero entire function a, we would like to find entire functions f and g such that a is a small function of f and g and the pair (f,g) satisfies the Pell type functional equation: f2+ag2=1. Such pair (f,g) is called an admissible entire solution and is studied for the first time in this note. We will show that all admissible solutions must be of certain form and they always exist. This will allow us to obtain some results on entire solutions of the related non-linear differential equation f2+a(f(k))2=1 where k is a positive integer. © 2019 |
| Persistent Identifier | http://hdl.handle.net/10722/278194 |
| ISSN | 2021 Impact Factor: 1.417 2020 SCImago Journal Rankings: 0.951 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Zhang, JJ | - |
| dc.contributor.author | Yang, CC | - |
| dc.contributor.author | Ng, TW | - |
| dc.date.accessioned | 2019-10-04T08:09:18Z | - |
| dc.date.available | 2019-10-04T08:09:18Z | - |
| dc.date.issued | 2019 | - |
| dc.identifier.citation | Journal of Mathematical Analysis and Applications, 2019, v. 480 n. 1, p. article no. 123240 | - |
| dc.identifier.issn | 0022-247X | - |
| dc.identifier.uri | http://hdl.handle.net/10722/278194 | - |
| dc.description.abstract | Given a non-zero entire function a, we would like to find entire functions f and g such that a is a small function of f and g and the pair (f,g) satisfies the Pell type functional equation: f2+ag2=1. Such pair (f,g) is called an admissible entire solution and is studied for the first time in this note. We will show that all admissible solutions must be of certain form and they always exist. This will allow us to obtain some results on entire solutions of the related non-linear differential equation f2+a(f(k))2=1 where k is a positive integer. © 2019 | - |
| dc.language | eng | - |
| dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmaa | - |
| dc.relation.ispartof | Journal of Mathematical Analysis and Applications | - |
| dc.subject | Entire admissible solutions | - |
| dc.subject | Non-linear differential equation | - |
| dc.subject | Pell type functional equations | - |
| dc.title | On admissible entire solutions of Pell type functional equation f2 + ag2 = 1 | - |
| dc.type | Article | - |
| dc.identifier.email | Ng, TW: ngtw@hku.hk | - |
| dc.identifier.authority | Ng, TW=rp00768 | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1016/j.jmaa.2019.06.011 | - |
| dc.identifier.scopus | eid_2-s2.0-85070195784 | - |
| dc.identifier.hkuros | 306792 | - |
| dc.identifier.volume | 480 | - |
| dc.identifier.issue | 1 | - |
| dc.identifier.spage | article no. 123240 | - |
| dc.identifier.epage | article no. 123240 | - |
| dc.identifier.isi | WOS:000483414100001 | - |
| dc.publisher.place | United States | - |
| dc.identifier.issnl | 0022-247X | - |