On a Problem Arising when Solving Equations with Singularities

Dmitry Kats


The article considers a problem that arises when solving equations with degenerating coefficients, specifically, the need to compute -Laplace-Borel transform of functions of the form . The paper shows that such problems can be reduced to equations with lesser cusp-type singularities. With the help of Laplace-Borel transform these equations are reduced to equations with regular singularities. Asymptotics of solutions to the latter are built as well as asymptotics of -Laplace-Borel transforms of initially considered functions.

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