All asymptotic expansions of solutions to the equation P6 in the case a·b=0

Abstract:

Here we consider the equation P6 for x→0 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·b≠0. Altogether for x→0 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→∞ and b=0 are obtained from the case a=0,
x→0 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·b≠0, a=0
and b=0. The last paragraph is dedicated to comparison of obtained results with known results.

Publication language:russian, pages:30

Research direction:

Mathematical problems and theory of numerical methods