共查询到20条相似文献,搜索用时 62 毫秒
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§1. IntroductionThispaperisconcernedwiththeasymptoticbehavioroftheoscillatorysolutionsofnonlin-earforcedneutraldelaydifferentialequationsoftheform[x(t)-∑mi=1pi(t)x(t-τi)]′ ∑nj=1qj(t)f(x(t-σj))=r(t), t≥t0,(1)wherepi,qj,r∈C([t0,∞),R),τi,σj≥0,i=1,2,…,m;j=1,2,…,n,f∈C(R,R),xf(x)>0forx≠0.Whenpi(t)≡0,i=1,2,…,m,Eq.(1)reducestox(t) ∑nj=1qj(t)f(x(t-σj))=r(t), t≥t0,(2)whoseasymptoticbehaviorofallsolutionshasbeenstudiedinJ.R.Yan[5].Whenr(t)≡0,f(x)≡xandm=n=1,Eq.(1)reducesto[… 相似文献
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考虑二阶非线性中立型时滞微分方程(x(t)-p(t)x(t-τ))″+∑ from i=1 to n (qi(t)fi(x(t-σi)))=0,t0,其中p,q_i∈C(R+,R+),τ,σ_i∈(0,∞),f_i∈C(R,R),i=1,2,…,n,分别得到了方程所有解振动和方程存在非振动解的充分条件,推广和改进了相关文献中的相关结果. 相似文献
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王克 《应用数学学报(英文版)》1998,(3)
Inthispaperweconsidernonlinear,nonautonomous,nonconvolutiontypeVolterrasystemoftheformForx=(x1,...,xn)∈Rn,wedefine.Weassumethat(A)Gi:R×R×Rn×Rn→R ismeasurableandthereexistsacontinuouspositivefunctionh:R-→ R suchthatandGi(t,s,0,0)≡0,andGi(t,s,x,y)is'nondecreasinginxjforfixedt,s,x1,...1xj-1,xj 1,...,xnandisnondecreasinginyiforfixedt,s,y1,...,yj-1,yj 1,...,yn,i,j=1,...,n.Wedefineandds,whereLetbethemetricspacewithop,Φ∈ChandeachofitscomponentsΦi(s)≥0fors≤0.Wealsoassumethatarecontin… 相似文献
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§ 1 IntroductionConsider the optimization problemmin{ f(x) :gj(x)≤ 0 ,j∈ I,gj(x) =0 ,j∈ L,x∈ Rn} ,(1 )where f(x) ,gj(x) :Rn→R,j∈I∪L.I={ 1 ,2 ,...,m} ,L={ m 1 ,...,m p} .We know thatthe sequential quadratic programming(SQP) [1~ 4] is one of the mostef-ficient methods to solve problem(1 ) because of its superlinear convergence.In order toovercome the Maratos effect[5] ,SQP should solve two quadratic sub-programmings ateachiteration,which,however,causes the amountof computation… 相似文献
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该文考虑多滞量和正负系数中立型方程[x(t)-sum from n=1 to l(1/n)C_A(t)x(t-r_n)] sum from i=1 to (1/i)P_i(t)x()t-τ_i)-sum from j=1 to n(1/j)Q_j(t)x(t-σ_j)=0,其中C_A(k=1,…,l),P_i(i=1,…,m),Q_j(j=1…,n)∈C([to,∞co),R~ ),0≤τ_l<…<τ_m,0≤σ_1<…<σ_n,0相似文献
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考虑多滞量非线性中立型微分方程其中τi,δj∈(0,∞),Pi,Qj∈C([l0,∞),R),i=1,2,…,m,j=1,2,…n,f∈C(R,R)且当x≠0时xf(x)>0,我们获得了方程本解一致稳定和渐近稳定的充分条件,改进和推广了文[6,8]等中相应结论. 相似文献
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该文利用一个严格集压缩不动点定理,得到了如下形式的一类时标上具状态依赖时滞的中立型泛函微分方程周期正解存在性的充分条件x~Δ(t)=x(t)[r(t)-a(t)x(t)-sum from j=1 to n a_j(t)x(t-Υ_j(t,x(t)))-sum from j=1 to n c_j(t)x~Δ(t-σ_j(t,x(t)))],其中r,a,a_j,c_j∈C(T,R~+)(j=1,2,…,n)是ω-周期函数,Υ_j,σ_j∈C(T×R,T)(j=1,2,…,n)分别是其第一变元的ω-周期函数. 相似文献
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A new second-order nonlinear neutral delay differential equation r(t) x(t) + P(t)x(t-τ) + cr(t) x(t)-x(t-τ) + F t,x(t-σ1),x(t-σ2),...,x(t-σn) = G(t),t ≥ t0,where τ 0,σ1,σ2,...,σn ≥ 0,P,r ∈ C([t0,+∞),R),F ∈ C([t0,+∞)×Rn,R),G ∈ C([t0,+∞),R) and c is a constant,is studied in this paper,and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according to the range of value of function P(t).Two examples are presented to illustrate that our works are proper generalizations of the other corresponding results.Furthermore,our results omit the restriction of Q1(t) dominating Q2(t)(See condition C in the text). 相似文献
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二阶非线性中立型时滞微分方程的振动准则 总被引:1,自引:0,他引:1
文章考虑二阶非线性中立型微分方程a(t)x(t)+∑li=1ci(t)x(t-τi(t))″+∑mi=1pi(t)fi(x(t-δi(t)))-∑ni=1qi(t)gi(x(t-σi(t)))=0的振动性,获得了该方程所有解振动的充分条件,推广了有关文献的结果. 相似文献
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本文对随机大系统dx(t)=b(t,x(t))dt σ(t,x(t)dω(t)采用较文[1]更一般的分解形式,利用比较法和分解-集结法得到该随机大系统随机(一致)稳定性和渐近(一致)稳定性的比较准则。 相似文献
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Paulo Xavier Pamplona 《Journal of Mathematical Analysis and Applications》2009,350(1):37-1087
In this paper we study the asymptotic behavior and the analyticity of the solutions of the one-dimensional porous-elasticity problem with thermal effect. Our main result is to prove the lack of exponential stability in case of the porous-elasticity with thermal effect when viscoelasticity is present. We prove the analyticity of the problem when a porous viscosity is present. We conclude by showing the impossibility of localization in time of the solutions in the isothermal case. 相似文献
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Burton Voorhees 《Complexity》2009,15(2):31-44
After a discussion of the importance of stability and instability for complex systems theory, we define the concept of virtual stability as a state in which a system employs self‐monitoring and adaptive control to maintain itself in a configuration that would otherwise be unstable. The energy expended in this gains the system an increase in its flexibility of behavioral response to environmental changes. A model designed to illustrate virtual stability is presented, followed by a brief discussion of the evolutionary advantage this capacity provides. This leads to the suggestion that such advantage gives an argument both for the directionality of evolution and for the emergence of self‐consciousness. © 2008 Wiley Periodicals, Inc. Complexity, 2009 相似文献
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利用Lyapunov泛函方法及线性矩阵不等式,得到了随机时滞混杂区间系统的能失性及鲁棒稳定性的充分判据。 相似文献
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In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results. 相似文献
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In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilinear differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results. 相似文献
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一类非线性动力系统实用稳定域的研究及应用 总被引:1,自引:0,他引:1
杨玉华 《数学的实践与认识》2012,42(13):189-192
借助于李雅普诺夫函数讨论了一类非线性动力系统的实用稳定性和实用稳定域的估计问题,得到了实用稳定域存在的充分条件,给出了一类动力系统实用稳定域的具体形式.通过具体实例说明了所给条件的实用性,改进了已有的结果. 相似文献
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Kojima's strong stability of stationary solutions can be characterized by means of first and second order terms. We treat the problem whether there is a characterization of the stability concept allowing perturbations of the objective function only, keeping the feasible set unchanged. If the feasible set is a convex polyhedron, then there exists a characterization which is in fact weaker than that one of strong stability. However, in general it appears that data of first and second order do not characterize that kind of stability. As an interpretation we have that the strong stability is the only concept of stability which both admits a characterization and works for large problem classes.Supported by the Deutsche Forschungsgemeinschaft, Graduiertenkolleg Analyse und Konstruktion in der Mathematik.Partial support under Support Center for Advanced Telecommunications Technology Research. 相似文献