On the solutions of multi-dimensional arbitrary order differential equation with mixed senior partial derivative and power-law non-linearities
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 41-49
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We study the solutions of a multi-dimensional differential equation of arbitrary order containing mixed senior partial derivative and power-law non-linearities on unknown function and its first derivatives. The method of functional separation of variables is applied for examining of this equation. The particular solutions of the equation under consideration are obtained. Some theorems which permit to decrease the order of this equation are proved.
@article{VMJ_2016_18_4_a4,
author = {I. V. Rakhmelevich},
title = {On the solutions of multi-dimensional arbitrary order differential equation with mixed senior partial derivative and power-law non-linearities},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {41--49},
publisher = {mathdoc},
volume = {18},
number = {4},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a4/}
}
TY - JOUR AU - I. V. Rakhmelevich TI - On the solutions of multi-dimensional arbitrary order differential equation with mixed senior partial derivative and power-law non-linearities JO - Vladikavkazskij matematičeskij žurnal PY - 2016 SP - 41 EP - 49 VL - 18 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a4/ LA - ru ID - VMJ_2016_18_4_a4 ER -
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I. V. Rakhmelevich. On the solutions of multi-dimensional arbitrary order differential equation with mixed senior partial derivative and power-law non-linearities. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 41-49. http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a4/