Analytic solutions of a second-order functional differential equation (Q2340816)
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| Language | Label | Description | Also known as |
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| English | Analytic solutions of a second-order functional differential equation |
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Analytic solutions of a second-order functional differential equation (English)
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21 April 2015
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The author establishes the existence of analytic solutions of the functional-differential equation \[ \alpha z+\beta x'(z)+\gamma x''(z)=x(az+bx''(z)), \quad z\in \mathbb{C}, \] where \(\alpha,\;\beta,\;\gamma,\;a,\;b\in \mathbb{C}\) and \(\gamma\neq 0\), by dealing with auxiliary equations obtained by appropriate transformations of the unknown function.
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iterative differential equation
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analytic solution
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resonance
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Brjuno condition
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