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Preprints of the Keldysh Institute of Applied Mathematics, 2007, 070, 30 pp. (Mi ipmp525)  

All asymptotic expansions of solutions to the equation P6 in the case $a\cdot b=0$

A. D. Bruno, I. V. Goryuchkina
Abstract: Here we consider the equation P6 for $x\to0$ and $a=0$. In that, we obtained 4 base families of expansions of its solutions different from base families of expansions of solutions for $a\cdot b\ne0$. Altogether for $x\to0$ and $a=0$ there exist 11 families of expansions of solutions involving expansions of four types: power, power-logarithmic, complicated and exotic. Most of them are new. Cases $a=0$, $x\to\infty$ and $b=0$ are obtained from the case $a=0$, $x\to0$ by means of reflections of symmetries of the equation. For $a=b=0$ there are absent expansions of solutions different from expansions of solutions for $a\cdot b\ne0$, $a=0$ and $b=0$. The last paragraph is dedicated to comparison of obtained results with known results.
Document Type: Preprint
UDC: 517.91
Language: Russian
Citation: A. D. Bruno, I. V. Goryuchkina, “All asymptotic expansions of solutions to the equation P6 in the case $a\cdot b=0$”, Keldysh Institute preprints, 2007, 070, 30 pp.
Citation in format AMSBIB
\Bibitem{BruGor07}
\by A.~D.~Bruno, I.~V.~Goryuchkina
\paper All asymptotic expansions of solutions to the equation P6 in the case $a\cdot b=0$
\jour Keldysh Institute preprints
\yr 2007
\papernumber 070
\totalpages 30
\mathnet{http://mi.mathnet.ru/ipmp525}
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    Препринты Института прикладной математики им. М. В. Келдыша РАН
     
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