Trigonometric Solutions of Nonlinear First-Order Ordinary Differential Equations over a Banach Algebra

被引：0

作者：

Derevenskii, V. P. ^{[1
]}

机构：

[1] Kazan State Architecture & Bldg Univ, Ul Zelyonaya 1, Kazan 420043, Russia

来源：

RUSSIAN MATHEMATICS | 2011年 / 55卷 / 09期

关键词：

differential equations; matrices; Lie algebras;

D O I：

10.3103/S1066369X11090040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we continue the study initiated in the recent paper (see Russian Mathematics (Iz. VUZ) 50 (8), 5-17 (2006)). We determine differentiation formulas for basic trigonometric functions and describe classes of nonlinear first-order ordinary differential equations (ODE.1) over a finite-dimensional Banach algebra whose solutions are the mentioned functions.

引用

页码：24 / 36

页数：13

共 10 条

[1]

Arnol'd V.I., 1971, ORDINARY DIFFERENTIA

[2]

Derevenskii V. P., 2006, RUSS MATH, V50, p[7, 5]

[3]

DEREVENSKII VP, 1987, IZV VUZ MAT+, P33

[4]

Eisenhart L.P., 1933, CONTINUOUS GROUPS TR

[5]

Jacobson N., 1962, LIE ALGEBRAS

[6]

JACOBSON N, 1964, LIE ALGEBRAS

[7]

Krein S. G., 1972, FUNCTIONAL ANAL SER

[8] ON THE EXPONENTIAL SOLUTION OF DIFFERENTIAL EQUATIONS FOR A LINEAR OPERATOR [J].

MAGNUS, W .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1954, 7 (04) :649-673

[9] EXPONENTIAL OPERATORS AND PARAMETER DIFFERENTIATION IN QUANTUM PHYSICS [J].

WILCOX, RM .

JOURNAL OF MATHEMATICAL PHYSICS, 1967, 8 (04) :962-&

[10]

Zaitsev V.F., 2001, HDB ORDINARY DIFFERE

← 1 →