Analytic Solutions of an Iterative Functional Differential Equation near Resonance
We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function 𝑥(𝑧)+𝑐𝑥(𝑧)=𝑥(𝑎𝑧+𝑏𝑥(𝑧)) in the complex field ℂ. By reducing the equation with the Schröder transformation to the another functional differential equation...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2009/145213 |
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| author | Tongbo Liu Hong Li |
| author_facet | Tongbo Liu Hong Li |
| author_sort | Tongbo Liu |
| collection | DOAJ |
| description | We investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function 𝑥(𝑧)+𝑐𝑥(𝑧)=𝑥(𝑎𝑧+𝑏𝑥(𝑧)) in the complex field ℂ. By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function 𝜆2𝑔(𝜆𝑧)𝑔(𝑧)−𝜆𝑔(𝜆𝑧)𝑔(𝑧) + 𝑐(𝑔(𝑧))2(𝜆𝑔(𝜆𝑧)−𝑎𝑔(𝑧)) = (𝑔(𝑧))3(𝑔(𝜆2𝑧)−𝑎𝑔(𝜆𝑧)), we get its local invertible analytic solutions. |
| format | Article |
| id | doaj-art-969171caa16c499fa48a17be99e7173f |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-969171caa16c499fa48a17be99e7173f2025-02-03T07:25:13ZengWileyInternational Journal of Differential Equations1687-96431687-96512009-01-01200910.1155/2009/145213145213Analytic Solutions of an Iterative Functional Differential Equation near ResonanceTongbo Liu0Hong Li1Department of Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaDepartment of Mathematics, Shandong University of Technology, Zibo, Shandong 255049, ChinaWe investigate the existence of analytic solutions of a class of second-order differential equations involving iterates of the unknown function 𝑥(𝑧)+𝑐𝑥(𝑧)=𝑥(𝑎𝑧+𝑏𝑥(𝑧)) in the complex field ℂ. By reducing the equation with the Schröder transformation to the another functional differential equation without iteration of the unknown function 𝜆2𝑔(𝜆𝑧)𝑔(𝑧)−𝜆𝑔(𝜆𝑧)𝑔(𝑧) + 𝑐(𝑔(𝑧))2(𝜆𝑔(𝜆𝑧)−𝑎𝑔(𝑧)) = (𝑔(𝑧))3(𝑔(𝜆2𝑧)−𝑎𝑔(𝜆𝑧)), we get its local invertible analytic solutions.http://dx.doi.org/10.1155/2009/145213 |
| spellingShingle | Tongbo Liu Hong Li Analytic Solutions of an Iterative Functional Differential Equation near Resonance International Journal of Differential Equations |
| title | Analytic Solutions of an Iterative Functional Differential Equation near Resonance |
| title_full | Analytic Solutions of an Iterative Functional Differential Equation near Resonance |
| title_fullStr | Analytic Solutions of an Iterative Functional Differential Equation near Resonance |
| title_full_unstemmed | Analytic Solutions of an Iterative Functional Differential Equation near Resonance |
| title_short | Analytic Solutions of an Iterative Functional Differential Equation near Resonance |
| title_sort | analytic solutions of an iterative functional differential equation near resonance |
| url | http://dx.doi.org/10.1155/2009/145213 |
| work_keys_str_mv | AT tongboliu analyticsolutionsofaniterativefunctionaldifferentialequationnearresonance AT hongli analyticsolutionsofaniterativefunctionaldifferentialequationnearresonance |