2019
Том 71
№ 7

# On the investigation of a integral manifold for a system of nonlinear equations, close to equations with variable coefficients, in a Hilbert space

Mitropolskiy Yu. A.

Abstract

The author considers a system of differential equations $$\frac{d\varphi}{dt} = \omega(t) + P(t, \varphi, h, \varepsilon)$$ $$\frac{dh}{dt} = H(t)h + Q(t, \varphi, h, \varepsilon)$$ where $h$ and $Q$ are vector functions with values in Hilbert space $H$, $\omega(t)$ is a limited operator function in Hilbert space $H$, for which the real parts of all points of the spectrum are negative. The existence and stability of a one-dimensional integral manifold for system (1) is proved with certain assumptions.

Citation Example: Mitropolskiy Yu. A. On the investigation of a integral manifold for a system of nonlinear equations, close to equations with variable coefficients, in a Hilbert space // Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 334-338.

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