共查询到20条相似文献,搜索用时 31 毫秒
1.
Cemil Tunç 《Journal of the Egyptian Mathematical Society》2012,20(1):43-45
The aim of this paper is to establish an instability theorem for a certain sixth order nonlinear delay differential equation. The proof of the theorem is based on the use of Lyapunov–Krasovskii functional approach. By this work, we improve an instability result obtained in the literature for a certain sixth order nonlinear differential equation without delay to the instability of the zero solution of a certain sixth order nonlinear delay differential equation. 相似文献
2.
Cemil Tun 《Annals of Differential Equations》2012,(1):11-14
This paper considers a kind of seventh order nonlinear differential equations with a deviating argument.By means of the Lyapunov direct method,some sufficient conditions are established to show the instability of the zero solution to the equation.Our result is new and complements the corresponding result of [5]. 相似文献
3.
本文研究了一类四阶非线性奇摄动方程的边界层问题,利用在左右边界层的两次匹配,得出了原问题解的一致有效的渐近表达式.这个结果是奇摄动理论在研究高阶微分方程中的一个应用. 相似文献
4.
M. Otelbaev A. A. Durmagambetov Ye. N. Seitkulov 《Proceedings of the Steklov Institute of Mathematics》2008,260(1):194-203
We study a nonlinear operator differential equation in a Hilbert space. This equation represents an abstract model for the system of Navier-Stokes equations. The main result consists in proving the existence of a strong solution to this equation under the condition that a certain other system of equations (related to the original equation) has only the zero solution. 相似文献
5.
一类三阶非线性微分方程解的不稳定性* 总被引:2,自引:0,他引:2
文献[1]讨论了非线性缓变系统的渐近稳定性,文献[2]讨论了三阶变系数线性微分方程解的不稳定性。本文应用文献[1]、[2]的方法讨论一类三阶非线性微分方程解的不稳定性。 相似文献
6.
7.
8.
9.
F. Tahamtani 《Journal of Applied Mathematics and Computing》1997,4(1):47-61
This paper is concerned with investigating the global asymptotic behavior of the zero solution of the initial-boundary value problem for a nonlinear fourth order wave equation. Moreover an estimate of the rate of decay of the solutions is obtained. 相似文献
10.
Sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions. The conditions assume the existence of a strong upper solution-lower solution pair, a concept that is defined in the paper. The differential equation has nonlinear dependence on all lower order derivatives of the unknown; in particular, appropriate Nagumo conditions are obtained and employed. 相似文献
11.
Mo Jiaqi 《数学年刊B辑(英文版)》1987,8(1):80-88
The singular perturbation for a boundary value problem of fourth order nonlinear differential equation is studied. Under suitable assumptions using differential inequalities the author finds a solution of the original problem and obtains the uniformly valid asymptotic expansions. 相似文献
12.
Eduardo Liz 《Journal of Mathematical Analysis and Applications》2005,303(2):492-498
We derive some explicit sufficient conditions for the asymptotic stability of the zero solution in a general linear higher order difference equation, and compare our estimations with other related results in the literature. Our main result also applies to some nonlinear perturbations satisfying a kind of sublinearity condition. 相似文献
13.
N.O. Sedova 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2324-2333
Some theorems on complete instability of the zero solution relative to a set for nonautonomous nonlinear equations with infinite delay are provided. The right-hand side of the equation is assumed to be defined in a fading memory space and to satisfy conditions that allow the construction of limiting equations. We use conceptions of Lyapunov-Razumikhin pairs and limiting equations to obtain new instability results, which are applicable, in particular, to autonomous, periodic and almost periodic in t delay differential equations. 相似文献
14.
Cemil Tunc 《Annals of Differential Equations》2006,22(1):7-12
In this paper, an instability criteria for nonlinear ordinary vector differential equation (1.1) is given. The result extends and includes the results of previous authors in ([1], [27]). 相似文献
15.
I. E. Vitrichenko 《Ukrainian Mathematical Journal》1999,51(6):934-941
We establish sufficient conditions for the Lyapunov instability of the trivial solution of a nonautonomous equation of thenth order in the case where its limit characteristic equation has a multiple zero root. The instability is determined by nonlinear
terms.
Odessa University, Odessa. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 835–841, June, 1999. 相似文献
16.
Manirupa Saha Amarendra K. Sarma 《Communications in Nonlinear Science & Numerical Simulation》2013,18(9):2420-2425
We report exact bright and dark solitary wave solution of the nonlinear Schrodinger equation (NLSE) in cubic–quintic non-Kerr medium adopting phase–amplitude ansatz method. We have found the solitary wave parameters along with the constraints under which bright or dark solitons may exist in such a media. Furthermore, we have also studied the modulation instability analysis both in anomalous and normal dispersion regime. The role of fourth order dispersion, cubic–quintic nonlinear parameter and self-steeping parameter on modulation instability gain has been investigated. 相似文献
17.
F.M. Mahomed Asghar Qadir 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):573-584
Lie’s invariant criteria for determining whether a second order scalar equation is linearizable by point transformation have been extended to third and fourth order scalar ordinary differential equations (ODEs). By differentiating the linearizable by point transformation scalar second order ODE (respectively third order ODE) and then requiring that the original equation holds, what is called conditional linearizability by point transformation of third and fourth order scalar ODEs, is discussed. The result is that the new higher order nonlinear ODE has only two arbitrary constants available in its solution. One can use the same procedure for the third and fourth order extensions mentioned above to get conditional linearizability by point or other types of transformation of higher order scalar equations. Again, the number of arbitrary constants available will be the order of the original ODE. A classification of ODEs according to conditional linearizability by transformation and classifiability by symmetry are proposed in this paper. 相似文献
18.
We consider the problem on nonzero solutions of the Schrödinger equation on the half-line with potential that implicitly depends on the wave function via a nonlinear ordinary differential equation of the second order under zero boundary conditions for the wave function and the condition that the potential is zero at the beginning of the interval and its derivative is zero at infinity. The problem is reduced to the analysis and investigation of solutions of the Cauchy problem for a system of two nonlinear second-order ordinary differential equations with initial conditions depending on two parameters. We show that if the solution of the Cauchy problem for some parameter values can be extended to the entire half-line, then there exists a nonzero solution of the original problem with finitely many zeros. 相似文献
19.
20.
A cubic spline method is described for the numerical solution of a two-point boundary value problem, involving a fourth order linear differential equation. This spline method is shown to be closely related to a known fourth order finite difference scheme. 相似文献