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2001•Journal of Jiangsu University of Science and TechnologyRequires access

Asymptotic Stability of a Class of Nonlinear Second Order Functional Differential Equation

Ping Zhang

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Abstract

By using the method of Lyapunov functional, the asymptotic stability of a class of nonlinear second order functional differential equation x″(t)+φ(x′(t),t)+f(x(t-r(t))) =0 is studied. Based on the lower boundness of the integral of |x′(t)|, a main lemma about x′(t) is obtained. The lower and upper bound of the ingegrals of φ(x′(t), t)/x′(t) are improved. Some new results are obtained. Some related results about the equation of linear, nonlinear, constant delay are generalized.

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What this paper is about

By using the method of Lyapunov functional, the asymptotic stability of a class of nonlinear second order functional differential equation x″(t)+φ(x′(t),t)+f(x(t-r(t))) =0 is studied. Based on the lower boundness of the integral of |x′(t)|, a main lemma about x′(t) is obtained. The lower and upper bound of the ingegrals of φ(x′(t), t)/x′(t) are improved. Some new results are obtained. Some related results about the equation of linear, nonlinear, constant delay are generalized.

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Available abstract

By using the method of Lyapunov functional, the asymptotic stability of a class of nonlinear second order functional differential equation x″(t)+φ(x′(t),t)+f(x(t-r(t))) =0 is studied. Based on the lower boundness of the integral of |x′(t)|, a main lemma about x′(t) is obtained. The lower and upper bound of the ingegrals of φ(x′(t), t)/x′(t) are improved. Some new results are obtained. Some related results about the equation of linear, nonlinear, constant delay are generalized.

Key concepts: Mathematics, Lemma (botany), Nonlinear system, Differential equation, Class (philosophy), Functional differential equation, Mathematical analysis, Order (exchange)

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