时间尺度上三阶Emden-Fowler中立型时滞动力方程的振动性和渐近性

伴随着科学技术的发展,时间尺度上动力方程的振动性研究在诸如种群动力学模型和电子工程、量子力学和航空航天科技工程中的Keller振荡模型的应用中有着越来越重要的作用.近年来,对时间尺度上二阶动力方程的研究已有许多成果,但对三阶动力方程的研究相对不够完善,因此对三阶动力方程振动性和渐进性的研究具有重要意义.本文研究一类时间尺度上三阶非线性中立型Emden-Fowler时滞动力方程的振动性和渐近性,利用Riccati变换及不等式技巧,建立了该类方程几个新的Leighton型,Kemenev型和Philos型振动准则,推广,改进和统一了已有文献中包括该类微分方程和差分方程的相关结果,并给出实例展示了本文主要结论的效果.     

三阶中立型时滞动力方程的振动性

本文首次研究时间尺度上一类新的二阶具有阻尼项的非线性时滞中立型动力方程的振动性的问题.利用时间尺度上的微积分理论、Riccati变换和不等式技巧的方法,获得方程振动的一些新的结果,推广已有文献的结果,丰富了三阶时滞动力方程的振动性.最后,通过例子验证了相关的结果.     

时标上一类三阶非线性中立型动力方程的振动性与渐近性

考虑了时标上一类三阶非线性中立型动力方程,得到了该方程一切解振动或渐近趋于零的充分条件.特别地,所得结果推广了一些已有的结论.     

测度链上一类三阶半线性中立型时滞动力方程的振动准则

利用广义Riccati代换及时标上一些分析技巧给出时标上一类三阶半线性动力方程的振动准则,并利用例子说明其结果的可用性,推广了一些已知的二阶或三阶动力方程振动性的结果.     

时标上的三阶非线性中立型变时滞动力方程的振动性与渐进性

考虑了时标上一类三阶非线性中立型变时滞动力方程的振动性和渐进性.利用Riccati变换技巧得到了方程所有解振动或渐进趋于零的充分条件.特别地,所得新结果发展了一些已有结论.并给出了例子加以说明本文的主要结果.     

时间尺度上三阶非线性中立型分布时滞动力方程的振动性

研究时间尺度上三阶非线性中立型分布时滞动力方程的振动性,利用广义Riccati变换和不等式技巧,建立了一个保证该方程每一个解振动或者收敛于零的充分性定理.本文所得定理推广和改进了已有文献中的相应结果.     

时标上三阶非线性时滞动力方程的振动性定理

本文研究时标上三阶非线性时滞动力方程的振动性,利用Riccati变换和不等式技巧,得到了较广泛的一类时滞动力方程的Leighton型, Philos型和Kamenev型振动定理,改进和推广了已有文献中的相应结果,并给出实例验证了所得结果的有效性.     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

带阻尼项的三阶强迫泛函微分方程的振动性和渐近性

建立了偏差变元依赖于状态的三阶强迫泛函微分方程解的若干振动性和渐近性.所得结果是新的,同时推广了文献中的有关结果.     

三阶非线性中立型微分方程的振动性和渐近性

本文的目的是研究三阶非线性中立型连续分布时滞微分方程■解的振动性和渐近性,其中f(x)/x~β≥δ0,x≠0且α0和β0均为正奇数之商.利用广义Riccati变换和积分平均技巧,我们对α≠β的情况,建立了一组保证方程每一解振动或者收敛到零的充分条件,所得结果改进和推广了最新文献中的一些熟知的准则,说明新结果应用的若干例子也被给出.     

Oscillatory and asymptotic criteria of third order nonlinear delay dynamic equations with damping term on time scales

In this paper, we are concerned with oscillatory and asymptotic behavior of third order nonlinear delay dynamic equations with damping term on time scales. By using a generalized Riccati function and inequality technique, we establish some new oscillatory and asymptotic criteria. The established results on one hand extend some known results in the literature, on the other hand unify continuous and discrete analysis as two special cases of an arbitrary time scale. We also present some applications for the established results.     

Oscillation and asymptotic behavior of third-order nonlinear neutral delay differential equations with distributed deviating arguments

This paper concerns the oscillation and asymptotic behavior of a class of third-order nonlinear neutral delay differential equations with distributed deviating arguments. By employing a generalized Riccati transformation and integral averaging technique, we establish some sufficient conditions to ensure that all solutions of the considered equations are either oscillatory or converge to zero, which extend and improve some known results in the literature.     

Oscillatory and Asymptotic Behavior for Second Order Quasilinear Difference Equations

1 IntroductionConsider the second order quasilinear difference equationA(g(Ay.--l)) + f(n,y.) = 0, for n E N(no), (l'l)where A is defined by Ay. = Vn+1--yn, n E N(no) = {no, no + 1,'' }, nO E N = {l, 2,'. }.The following hold throughout the paPer:(H0) (i) g: R-R is a continuous increasing fUnction with propertiessgng(y) = sgny) g(R) = R;(il) f: N(no) x R--+ R is continuous as a function of y E R;(iii) yf(n,y) > 0 for n E N and y / 0.By a solution of the equation (1.l) we mean a non…     

STABILITY OF SOLUTIONS OF FIRST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH OSCILLATORY COEFFICIENTS

ＳＴＡＢＩＬＩＴＹＯＦＳＯＬＵＴＩＯＮＳＯＦＦＩＲＳＴＯＲＤＥＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＯＳＣＩＬＬＡＴＯＲＹＣＯＥＦＦＩＣＩＥＮＴＳ￥ＷａｎｇＱｉｒｕ(王其如）（ＬｕｏｙａｎｇＴｅａｃｈｅｒ?..     

Oscillation of Third-order Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.     

Weakly Nonlinear Oscillatory Waves with Multi-phases in Ideal Incompressible Fluid

In this paper, we apply the technique of weakly nonlinear geometric optics to study weakly nonlinear oscillatory waves with multi-phases in d-dimensional ideal incompressible fluid for d ≥ 2. Precisely, we give a rigorous asymptotic expansion for the solution of the oscillatory initial value problem to the ideal incompressible Euler equations. Generally, this problem is not well posed. However, the coherence assumption and small divisor property imposed on the phases functions lead to a compatibility condition for the solvability of profile equations from which we can determine every profile.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF HIGHER ORDER NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our results generalize and improve the previous results.     

OSCILLATION OF THIRD ORDER DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses.Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.     

Oscillatory region and asymptotic solution of fractional van der Pol oscillator via residue harmonic balance technique

In this paper, a powerfully analytical technique is proposed for predicting and generating the steady state solution of the fractional differential system based on the method of harmonic balance. The zeroth-order approximation using just one Fourier term is applied to predict the parametric function for the boundary between oscillatory and non-oscillatory regions of the fractional van der Pol oscillator. The unbalanced residues due to Fourier truncation are considered iteratively by solving linear algebraic equations to improve the accuracy of the solutions successively. The highly accurate solutions to the angular frequency and limit cycle of fractional van der Pol oscillator are obtained and compared. The results reveal that the technique described in this paper is very effective and simple for obtaining asymptotic solution of nonlinear system having fractional order derivative.