Trigonometric solutions of nonlinear first-order ordinary differential equations over a Banach algebra

V. P. Derevenskii

Chair of Higher Mathematics, Kazan State Architecture and Building University, Kazan, Russia

Abstract: 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.

Keywords: differential equations, matrices, Lie algebras.

UDC: 517.983

Received: 12.07.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:9, 24–36

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