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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9643 1687-9651 |