Non-linear Differential EquationsPergamon Press; [distributed in the Western Hemisphere by Macmillan, New York], 1964 - Differential equations - 535 pages |
Contents
Lipschitzian and Carathéodory Systems | 11 |
The Solution ttox of the System 1 1 | 17 |
Periodic Solutions | 25 |
Copyright | |
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a₁ arbitrary assume asymptotic stability b₁ behavior belonging bounded boundedness c₁ C₂ class C¹ Consequently consider constant continuous corresponding d₁ defined denote differential equations differenziale dy/dx finite number following theorem function given holomorphic homogeneous homogeneous polynomials hypotheses ibid inequality integral curve isolated singular point J. E. Littlewood J. L. Massera L. E. J. Brouwer Lemma Levinson Liénard limit cycle Lipschitzian Math matrix neighborhood node nonlinear oscillations P₁ periodic solutions phase plane plane Poincaré polynomials prove R₁ reduced system respect roots Russian saddle point Sansone satisfies the conditions sector separatrices solution x(t sufficiently small Suppose system x t₁ t₂ tangent trajectories tending type numbers u₁ uniqueness unstable v₁ whence x-axis x(to x₁ y(to y₁ zero