2003•Ha'erbin gongye daxue xuebaoRequires access

Boundedness and asymptotic behavior of solutions of second order nonlinear differential equation

Ying Liu

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Abstract

The boundedness and asymptotic characteristic of solutions of second order nonlinear differential equation(a(t)x′)′+f(t,x,x′)=0 is considered by using the integral inequality. Some important results obtained generalize and improve some of the previous results. a(t) that is defined on +=[0,+∞)is positive function, and∫ ∞ 0[SX(]1a(t) d t∞, f(t,x,y) that are defined on R +×R×R are continous function.

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The boundedness and asymptotic characteristic of solutions of second order nonlinear differential equation(a(t)x′)′+f(t,x,x′)=0 is considered by using the integral inequality. Some important results obtained generalize and improve some of the previous results. a(t) that is defined on +=[0,+∞)is positive function, and∫ ∞ 0[SX(]1a(t) d t∞, f(t,x,y) that are defined on R +×R×R are continous function.

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Available abstract

The boundedness and asymptotic characteristic of solutions of second order nonlinear differential equation(a(t)x′)′+f(t,x,x′)=0 is considered by using the integral inequality. Some important results obtained generalize and improve some of the previous results. a(t) that is defined on +=[0,+∞)is positive function, and∫ ∞ 0[SX(]1a(t) d t∞, f(t,x,y) that are defined on R +×R×R are continous function.

Key concepts: Mathematics, Nonlinear system, Order (exchange), Function (biology), Mathematical analysis, Differential equation, Differential (mechanical device), Pure mathematics

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