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- W2799683439 abstract "A Functional equation $sum_{i=1}^{m}a_{i}(z)u(varphi_{i}(z))=f(z)$ is considered. First we show the existence of solutions of formal power series. Second we study the homogeneous equation $(f(z)equiv 0)$ and construct formal solutions containing exponential factors. Finally it is shown that there exists a genuine solution in a sector whose asymptotic expansion is a formal solution, by using the theory of Borel summability of formal power series. The equation has similar properties to those of irregular singular type in the theory of ordinary differential equations." @default.
- W2799683439 created "2018-05-17" @default.
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- W2799683439 date "2018-04-01" @default.
- W2799683439 modified "2023-09-24" @default.
- W2799683439 title "A functional equation with Borel summable solutions and irregular singular solutions" @default.
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- W2799683439 doi "https://doi.org/10.2969/jmsj/07027491" @default.
- W2799683439 hasPublicationYear "2018" @default.
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