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.

Full Text:

PDF (Russian)


Kac D.S. Vychislenie asimptotik reshenij uravnenij s polinomial'nymi vyrozhdenijami kojefficientov. // Differenc. uravnenija. 2015. T. 51. # 12. S. 1612–1617.

Korovina M.V., Shatalov V.E. Differencial'nye uravnenija s vyrozhdeniem i resurgentnyj analiz. // Differenc. uravnenija. 2010. T. 46. # 9. S. 1259–1277.

Korovina M.V. Asimptotiki reshenij neodnorodnyh uravnenij so starshimi vyrozhdenijami. // Differenc. uravnenija. 2013. T. 49. # 2. S. 255–259.

Volnuhin M.M. Asimptotiki reshenij differencial'nyh uravnenij s vyrozhdenijami v sluchae rezonansa. // DAN. 2013. T. 449. # 3. S. 259–262.

F.W.J. Olver. Asymptotics and Special Functions. Academic Press. 1974.

Korovina M.V. Metod povtornogo kvantovanija i ego primenenija k postroeniju asimptotik reshenij uravnenij s vyrozhdenijami. // Differenc. uravnenija. 2016. T. 52. # 1. S. 60–77.

Sternin B., Shatalov V. Borel-Laplace Transform and Asymptotic Theory. Introduction to Resurgent Analysis. CRC Press, 1996.

Korovina M.V. Asimptotiki reshenij uravnenij s vysshimi vyrozhdenijami. // DAN. 2011. T. 437. # 3, S. 302–304.

Korovina M.V. Teorija funkcional'nyh prostranstv i differencial'nye uravnenija. Moskva, 2007.

Korovina M.V. Cushhestvovanie resurgentnogo reshenija dlja uravnenij s vyrozhdeniem vysshih porjadkov. // Differenc. uravnenija. 2011. T. 47. # 3. S. 349–357.


  • There are currently no refbacks.

IT-EDU-2017   Servletsuite

ISSN: 2307-8162