Boundedness and asymptotic behavior of solutions of second order nonlinear differential equation
Ying Liu
Abstract
Ying Liu
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.
Key concepts: Mathematics, Nonlinear system, Order (exchange), Function (biology), Mathematical analysis, Differential equation, Differential (mechanical device), Pure mathematics