Abstract
We study the existence of resurgent solutions of differential equations with higher-order degeneration. The proof of the existence of a resurgent solution for the case in which the right-hand side of the equation is a resurgent function is the main result of the present paper.
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Schulze, B.-W., Sternin, B., and Shatalov, V., Operator Algebras Associated with Resurgent Transforms and Differential Equations on Manifolds with Singularities, in Spectral Theory, Microlocal Analysis, Singular Manifolds, Academie Verlag, 1997, pp. 334–364.
Korovina, M.V. and Shatalov, V.E., Differential Equations with Degeneration and Resurgent Analysis, Differ. Uravn., 2010, vol. 46, no. 9, pp. 1259–1277.
Sternin, B. and Shatalov, V., Borel-Laplace Transform and Asymptotic Theory. Introduction to Resurgent Analysis, CRC, 1996.
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Original Russian Text © M.V. Korovina, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 3, pp. 349–357.
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Korovina, M.V. Existence of resurgent solutions for equations with higher-order degeneration. Diff Equat 47, 346–354 (2011). https://doi.org/10.1134/S0012266111030050
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DOI: https://doi.org/10.1134/S0012266111030050