For a certain class of nonlinear homogeneous difference equations, it is shown that every nonoscillatory entire solution xn has exponential bounds on Z and that the oscillation is equivalent to the nonexistence of pos...For a certain class of nonlinear homogeneous difference equations, it is shown that every nonoscillatory entire solution xn has exponential bounds on Z and that the oscillation is equivalent to the nonexistence of positive real characteristic roots. Explicit conditions for oscillation in terms of coefficients are also obtained.展开更多
<正> 1960年,波兰数学家Z.Opial证明了:若f(t)是绝对连续函数,f(0)=0,则 integral from n=0 to α(|f(t)||f'(t)|dt)≤α/2 integral from n=0 to α (|f'(t)|~2dt), α>0,(1)且等式仅当f(f)=kt(k是常数)时成立之后,...<正> 1960年,波兰数学家Z.Opial证明了:若f(t)是绝对连续函数,f(0)=0,则 integral from n=0 to α(|f(t)||f'(t)|dt)≤α/2 integral from n=0 to α (|f'(t)|~2dt), α>0,(1)且等式仅当f(f)=kt(k是常数)时成立之后,引起了许多人的注意,并得到了多种推广与改进。但这些工作都是(?)对单变元函数而作的。直到1982年。展开更多
In this paper, we obtain the boundedness, asymptotic behavior and oscillatory properties for the single logistic models with impulse effect. Some examples are given to indicate the application of our results.
文摘For a certain class of nonlinear homogeneous difference equations, it is shown that every nonoscillatory entire solution xn has exponential bounds on Z and that the oscillation is equivalent to the nonexistence of positive real characteristic roots. Explicit conditions for oscillation in terms of coefficients are also obtained.
文摘<正> 1960年,波兰数学家Z.Opial证明了:若f(t)是绝对连续函数,f(0)=0,则 integral from n=0 to α(|f(t)||f'(t)|dt)≤α/2 integral from n=0 to α (|f'(t)|~2dt), α>0,(1)且等式仅当f(f)=kt(k是常数)时成立之后,引起了许多人的注意,并得到了多种推广与改进。但这些工作都是(?)对单变元函数而作的。直到1982年。
基金the National Natural Science Fundation of China (No.10071043).
文摘In this paper, we obtain the boundedness, asymptotic behavior and oscillatory properties for the single logistic models with impulse effect. Some examples are given to indicate the application of our results.
