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- Title
Asymptotics solutions of equations with higher-order degeneracies.
- Authors
Korovina, M. V.
- Abstract
The article discusses the difficulties involved in constructing asymptotic expansions for solutions of equations with higher-order degeneracies. It emphasizes the applications of differential equations in studying solutions of equations on manifolds with conical singularities and equations with beak-type singular points. It mentions the use of the Laplace-Borel transform as the basic technical tool for constructing the theory of resurgent functions. It offers details on the basic notions of resurgent function based on the application of the Laplace-Borel transform. Several formulas for solving differential equations are also provided.
- Subjects
ASYMPTOTIC theory of algebraic ideals; DIFFERENTIAL equations; NUMERICAL analysis; DEGENERATE differential equations; DIFFERENTIABLE manifolds; DIFFERENTIAL geometry; LAPLACE transformation; BOREL sets; NUMERICAL solutions to equations; MATHEMATICAL formulas
- Publication
Doklady Mathematics, 2011, Vol 83, Issue 2, p182
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562411020165