一类微分方程零解全局弱吸引和全局吸引到充要条件

Abstract

Abstract:

This paper deals with the global weak attractivity and global attractivity for the nonlinear differential equations
x = φ（y）-F(x), {y}=- g(x)q(y).
It is shown that Filippov condition (A₂) cannot exclude the existence of the maximum elliptic sector S^* and it cannot exclude the possibility of ∂S^* as the ω-limit set of the orbits departing from the exterior of S^*. The problem proposed by Jiang Jifa in Nonlinear Analysis, 28(5), 855--870(1997) is answered by a negative answer. A series of necessary and sufficient conditions for the global weak attractivity and global attractivity are established for both the cases that Filippov condition holds and Filippov condition fails. Some new conditions for the global asymptotic stability are also obtained.

Key words: Filippov condition, Global attractivity, Global , weak , attractivity, Global , asymptotic stability

CLC Number:

34D05

ZHAO Li-Qin. Necessary and Sufficient Conditions for the Global Weak Attractivity and Global Attractivity of a Class of Nonlinear Differential Equations[J].Acta mathematica scientia,Series A, 2009, 29(3): 529-537.

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Necessary and Sufficient Conditions for the Global Weak Attractivity and Global Attractivity of a Class of Nonlinear Differential Equations

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