共查询到20条相似文献,搜索用时 0 毫秒
1.
靳明忠 《应用数学和力学(英文版)》1994,15(9):867-875
OSCILLATIONTHEOREMSOFHIGHERORDERNONLINEARDELAYDIFFERENTIALEQUATIONSJinMing-zhong(靳明忠)(DepartmentofBasicCourses,YunnanInstitut... 相似文献
2.
In this paper,using a fixed point principle and existence principle given in[1],westudy the boundary value problems for second order differential equations.Some newexistence results are obtained. 相似文献
3.
David E. Gilsinn 《Nonlinear dynamics》2007,50(1-2):73-92
In this paper, we prove a result that says: Given an approximate solution and frequency to a periodic solution of an autonomous
delay differential equation that satisfies a certain noncriticality condition, there is an exact periodic solution and frequency
in a neighborhood of the approximate solution and frequency and, furthermore, numerical estimates of the size of the neighborhood
are computed. Methods are outlined for estimating the parameters required to compute the errors. An application to a Van der
Pol oscillator with delay in the nonlinear terms is given. 相似文献
4.
We prove an approximation result for the solutions of a singularly perturbed, nonautonomous ordinary differential equation which has interesting applications to problems in higher dimensions. Here our result is applied to a singularly perturbed, delay differential equation with state dependent time-lags (i.e., aninfinite dimensional problem). We find a new dynamical system (also in infinite dimensions), which describes, in a certain sense, the dynamics of our delay equations for very small values of the singular parameter. 相似文献
5.
王培光 《应用数学和力学(英文版)》1999,20(6):698-704
IntroductionOwingtotheextensiveapplicationofneutralequations,moreandmorestudieshavebenmadeonthebehaviorofthesolutions[1,2].Fo... 相似文献
6.
FORCEDOSCILLATIONSOFBOUNDARYVALUEPROBLEMSOFHIGHERORDERFUNCTIONALPARTIALDIFFERENTIALEQUATIONSJinMingZhong(靳明忠),DongYing(董莹),Li... 相似文献
7.
The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied. The stability behavior of Rosenbrock method was analyzed for the solutions of linear test equation. The result that the Rosenbrock method is GP-stable if and only if it is A-stable is obtained. 相似文献
8.
Consider the perturbed nonautonomous linear delay differential equation x(t) = - a(t)x(t-τ) + F(t, x1, t ⩾ 0 where x1(s)=x(t+s) for −δ≤s≤0. Suppose that a(t) ∈ C([0,∞), (0,∞)), τ≥0,F:[0, ∞) x C[−δ,0] → R is a continuous functions and F(t,0)
≡ 0. Here C[−δ,0] is the space of continuous functions Φ: [−δ,0] → R with ∥Φ∥<H for the norm | Φ |, where |·| is any norm
in R and 0<H≤+∞.
Most of the known papers [1–5,7] have been concerned with the local or global asymptotic behavior of the zero solution of
Eq. (*) when a(t) is independent of t i. e., a(t) is autonomous. The aim in this paper is to derive the sufficient conditions
for the global attractivity of the zero solution of of Eq. (*) When a(t) is nonautomous. Our results, which extend and improve
the known results, are even “sharp”. At the same time, the method used in this paper can be applicable to the perturbed nonlinear
equation.
Project supported by the Natural Science Foundation of Hunan 相似文献
9.
林文贤 《应用数学和力学(英文版)》1997,18(8):789-800
I.IntroductionAstheoscillatorybehaviorandasymptoticbehavioroffunctionaldifferentialequations'solutionsareveryimportantbothintheoryandpractice,lotsofreseachresultshavecomeoutinthisfieldinrecentyears.Indocument[l1,theoscillationandasymptoticclassificationof… 相似文献
10.
IntroductionAsweknow ,intheinvestigationofthepropertiesofsolutionsfornonlineardifferentialequations,themethodofvariationofparametersisaneffectivetoolinthecasethatthecorrespondingunperturbedtermsarelinearorofcertainsmoothnessthoughtheyarenonlinear.Onthe… 相似文献
11.
Oscillatory properties of the solutions of nonlinear delay hyperbolic differential equations of neutral type 总被引:2,自引:0,他引:2
Thenewly—developedtheoryofnonlineardelaypartialfunctionaldifferentialequationsareappliedinmanyfields,suchasinengineering ,biology,medicine,physicsandchemistry .Aseriesofsufficientconditions,necessaryandsufficientconditionsforoscillationsoftheequationswer… 相似文献
12.
Cemil Tunc 《应用数学和力学(英文版)》2006,27(8):1141-1148
By the use of the Liapunov functional approach, a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay. The established result is less restrictive than those reported in the literature. 相似文献
13.
ARC-length method for differential equations 总被引:1,自引:0,他引:1
IntroductionTheordinaryandpartialdiferentialequationsofcontinuumproblemareoftenwithcertaintypesofsingularityasstifproperty,or... 相似文献
14.
Mirosław Lachowicz 《Nonlinear dynamics》1994,5(3):393-399
A finite system of stochastic interacting particles is considered. The system approximates the solutions of the kinetic equations (the Boltzmann equation, the Boltzmann-Enskog equation) as well as the solutions describing the macroscopic evolution of fluids: the Euler and the Navier-Stokes hydrodynamic equations. 相似文献
15.
Transition layers for singularly perturbed delay differential equations with monotone nonlinearities
Shui-Nee Chow Xiao-Biao Lin John Mallet-Paret 《Journal of Dynamics and Differential Equations》1989,1(1):3-43
Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heteroclinic orbit, and that this orbit is monotone. The proof involves a global continuation for heteroclinic orbits. 相似文献
16.
Michael C. Mackey Irina G. Nechaeva 《Journal of Dynamics and Differential Equations》1994,6(3):395-426
We study the stability of linear stochastic differential delay equations in the presence of additive or multiplicative white and colored noise. Using a stochastic analog of the second Liapunov method, sufficient conditions for mean square and stochastic stability are derived. 相似文献
17.
刘玉记 《应用数学和力学(英文版)》2002,23(3):355-362
IntroductionConsidertheglobalattractivityofthenonlineardelaydifferenceequationΔxn+anxn+f(n ,∑0s=-k qs,nxs+n) =0 (n=0 ,1 ,2 ,… ) . ( 1 )TheinitialvalueofEq .( 1 )isxs =φs (s=-k ,-k+ 1 ,… ,-1 ,0 ) . ( 2 )Inthesequel,wealwayssupposethatD1) an isanonnegativerealsequence ,0 ≤an <1andkisapositive… 相似文献
18.
黄先开 《应用数学和力学(英文版)》1999,20(10):1116-1120
IntroductionIntherecentyears,withalotofapplicationsofneuralnetworkmodels,manyauthors[1~3]areinterestedintheresearchofthestructureandperformanceforthesenetworks.BecauseHopfieldneuralnetworkwellsimulatetheecologicalsystem,manystudiesareconcentratedonth… 相似文献
19.
In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results. 相似文献
20.
Aldo Rustichini 《Journal of Dynamics and Differential Equations》1989,1(2):121-143
Functional differential equations of mixed type (MFDE) are introduced; in these equations of functional type, the time derivative may depend both on past and future values of the variables. Here the linear autonomous case is considered. We study the spectrum of the (unbounded) operator, and construct continuous semigroups on the stable, center, and unstable subspaces. 相似文献