Boundedness in Asymmetric Quasi-periodic Oscillations

In the paper, by applying the method of main integration, we show the boundedness of the quasi-periodic second order differential equation x′′+ ax~+-bx~-+φ(x) = p(t), where a≠b are two positive constants and φ(s), p(t) are real analytic functions. Moreover, the p(t) is quasi-periodic coefficient, whose frequency vectors are Diophantine. The results we obtained also imply that, under some conditions,the quasi-periodic oscillator has the Lagrange stability.     

Invariant Tori and Boundedness in Asymmetric Oscillations

In this paper,we are concerned with the boundedness of all the solutions of the equation x″ ax^ -bx- Ф(x)=p(t),where p(t) is a smooth 2π-periodic function,a and b are positive constants,and the perturbation Ф(x) is bounded.     

Boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem

In this paper we consider the boundedness of all the solutions for the equation x″ + ax ⁺−bx ⁻ = f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b). Received November 27, 1998, Accepted October 15, 1999     

非对称振动中解的有界性

在本文中,我们考虑方程x″+ax~+-bx~-=f(t)的所有解的有界性,其中f(t)是一个光滑2π-周期函数,a和b是正的常数(a≠b).     

Existence of Periodic Solutions in Nonlinear Asymmetric Oscillations

The existence of periodic solutions for the nonlinear asymmetricoscillator x' + x⁺ – rßx^– = h(t),(' =d/dt (is discussed, where , rß are positive constantssatisfying for some positive integer n N and h(t) L (0,2) is 2-periodic with x^±= max {±x,0}. 2000 Mathematics Subject Classification34C10, 34C25.     

非线性时滞差分方程的线性化振动性

本文建立了非线性时滞差分方程的线性化振动性的结果,推广了文[1]的工作．     

双非线性抛物组解的有界性

本文考虑对角型双非线性抛物型方程组，在一般结构条件下，证明广义解局部有界和整体有界，并对一特殊情形，证明了如果解在抛物边界为零，那么它只能是零解．     

二阶非线性脉冲微分方程的振动性

考虑二阶脉冲微分方程(r(t)(x′(t))σ)′+f(t,x(t),x′(t))=0,t t0,t≠tk,k=1,2,…x(tk+)=gk(x(tk)),x′(tk+)=hk(x′(tk)),k=1,2,…(E)其中0 t0相似文献   

二阶非线性微分方程的振动性

本文利用Riccati技巧和平均技巧，研究一类二阶非线性微分方程的振动性，得到了这类方程振动的若干新的判别准则。     

n阶非线性中立型微分方程的振动性(英文)

本文获得了一类具连续偏差变元的偶数阶非线性中立型泛函微分方程所有解振动的若干充分条件 .     

Boundedness and Global Nonexistence for a Nonlinear Convective Parabolic-System

A two-component parabolic system with convective terms is studied. It is shown that if the forces on the right hand side are no worse than quadratic in the variables then the solution remains bounded for all time. It is also proved that if the forces are allowed to grow faster than quadratic then finite time blow-up is to be expected.     

一类一阶非线性中立型微分方程的振动性

讨论了一类一阶非线性中立型微分方程的振动性问题,得到了其具有振动解的“sharp”条件.     

Oscillations of Second Order Nonlinear Neutral Differential Equations

ＯｓｃｉｌｌａｔｉｏｎｓｏｆＳｅｃｏｎｄＯｒｄｅｒＮｏｎｌｉｎｅａｒＮｅｕｔｒａｌＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓＷａｎｄＯｉｒｕ；（王其如）ＷｕＹｅｗｅｉ（武业伟）（ＬｕｏｇａｎｇＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｌｕｏｙａｎｇ４７１０２...     

非线性二阶中立型微分方程的振动性

考虑中立型微分方程我们建立了方程(1)的若干振动准则。这些结果适用于强超线性和强次线性中立型微分方程,且当p(t)≡0时仍然成立。     

Oscillations of Second Order Nonlinear ODE with Impulses

§ 1.Introduction　 There are a lot of good results on the oscillations of classical second-order nonlinearODE(see[1 ,2 ,3 ] ) ,but few of them are on second-order nonlinear ODE with impuls-es. Very recently,Chen and Feng[4] studied the following second-order nonlinear ODEwith impulses:x″(t) + f(t,x(t) ) =0 ,x(t+k ) =g(x(tk) ) ,x(t+0 ) =x0 ,　　t≥ t0 ,t≠ tk,k =1 ,2 ,… ,x′(t+k ) =hk(x′(tk) ) ,k =1 ,2 ,… ,x′(t+0 ) =x′0 ,(1 )and they obtained some interesting results about Eq. (1 ) .…     

非线性振动中两变量型尺度法存在的问题与改进

本文指出了非线性振动中两变量型尺度法存在的问题并进行了改进.最后证明了改进的两变量型尺度法与КВМ法等价.     

Periodic Oscillations and Waves in Nonlinear Weakly Coupled Dispersive Systems

Bifurcations of periodic solutions in autonomous nonlinear systems of weakly coupled equations are studied. A comparative analysis is carried out between the mechanisms of Lyapunov–Schmidt reduction of bifurcation equations for solutions close to harmonic oscillations and cnoidal waves. Sufficient conditions for the branching of orbits of solutions are formulated in terms of the Pontryagin functional depending on perturbing terms.     

具有非线性扩散项的多维趋化趋触模型的整体有界性

本文主要研究一类带有齐次Neumann边界条件且具有非线性扩散项的趋化趋触模型,在较宽的条件下,证明了系统具有整体有界古典解.推广了XU等(2019)和JIA等(2020)得到的整体有界的古典解的结论.