共查询到20条相似文献,搜索用时 0 毫秒
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In this paper the authors study the oscillation and the asymptotic behavior of solutiosn to the second-order nonlinear differential equations
$[\ddot x]\pmX(t,x,[\dot x])=0$(X_{\pm})
and give necessary and sufficient conditions for Equation (X_+) to have a bounded nonoscillatory solution or to be oscillatory. There are four classes of solutions to Equation (X_) with different asymptotic behavior. For each class of solution, the necessary or sufficient condition of the existence is obtained. 相似文献
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一类具有脉冲的非线性时滞微分方程解的渐进性 总被引:2,自引:0,他引:2
研究了-类具有脉冲的二阶非线性时滞微分方程 (r(t))X'-p(t)x'(t) n∑i=1 qi(t)x(t-σi) f(t)=0, t≠tk, x(t k)-x(tk)=akx(tk),x1(t k)-x1(tk)=bkx1(tk), k∈z 的解的渐近性,并得到了一系列相关的充分条件. 相似文献
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We establish conditions for the existence and uniqueness of continuous asymptotically periodic solutions of nonlinear difference equations with continuous argument. 相似文献
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Oscillatory and Asymptotic Behavior of Solutions for Nonlinear Impulsive Delay Differential Equations 总被引:1,自引:0,他引:1
Wei-hua Mao An-hua Wan 《应用数学学报(英文版)》2006,22(3):387-396
The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established, Three illustrative examples are proposed to demonstrate the effectiveness of the conditions. 相似文献
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In this paper, the initial value problem for the drift-diffusion equation which stands for a model of a semiconductor device is studied. When the dissipative effect on the drift-diffusion equation is given by the half Laplacian, the dissipation balances to the extra force term. This case is called critical. The goal of this paper is to derive decay and asymptotic expansion of the solution to the drift-diffusion equation as time variable tends to infinity. 相似文献
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建立了三阶非线性微分方程…x+φ(x,x.,¨x)¨x+f(x,x.)=p(t,x,x.,¨x)的一切解有界和收敛到零的充分条件. 相似文献
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A mixed problem with acoustic transmission conditions for nonlinear hyperbolic equations with nonlinear dissipation is considered. The existence, uniqueness, and exponential decay of global solutions to this problem with focusing nonlinear sources are proved Additionally, the existence of global solutions and the solution blow-up in a finite time are proved for the case of defocusing nonlinear sources. 相似文献
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本文研究一类非线性高阶发展方程ua-△ui,-0△ua-△i=f(u)整体强解的渐近行为,利用ω极限紧方法得到了整体强解的全局吸引子 的存在性, 在D(A)×D(A)不变、紧,并且按D(A)×D(A)的范数吸引D(A)×D(A)中的任意有界集,其中非线性项f满足临界指数增长条件. 相似文献
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将讨论的差分方程△(rm-1x0-1)+qnxn=anf(xn)看成是其对应的齐次差分方程Δ(rn-1Δyn-1)+qnyn=0的非线性扰动,其中f(x)为[0,∞)连续函数.设对应的齐次差分方程非振动,zn和yn为其主解和非主解.本文将运用压缩映象原理,获得方程存在渐近于其对应齐次方程主解的解的充分条件.并用方程的系数给出其渐近的精确表示. 相似文献
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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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Yang Jinshun 《东北数学》1995,(2)
The Asymptotic Behavior of Solutions of Some Doubly Degenerate Nonlinear Parabolic EquationsYangJinshun(杨金顺)(DepartmentofBasi... 相似文献
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本文主要讨论一类带p(1 2n/(n 2)■p<3)幂增长耗散位势的非牛顿流体模型解的渐近性态,利用改进的Fourier分解方法,证明了其解在L~2范数下衰减率为(1 t)~(-n/4). 相似文献
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本文主要讨论一类带 $p \,\,( 1+\frac{2n}{n+2} \leq p<3 )\,$ 幂增长耗散位势的非牛顿流体模型解的渐近性态, 利用改进的 Fourier分解方法, 证明了其解在$L^2$ 范数下衰减率为 $(1+t)^{-\frac{n}{4}}$. 相似文献
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Asymptotic Behavior of Solutions of Dynamic Equations 总被引:1,自引:0,他引:1
We consider linear dynamic systems on time scales, which contain as special cases linear differential systems, difference systems, or other dynamic systems. We give an asymptotic representation for a fundamental solution matrix that reduces the study of systems in the sense of asymptotic behavior to the study of scalar dynamic equations. In order to understand the asymptotic behavior of solutions of scalar linear dynamic equations on time scales, we also investigate the behavior of solutions of the simplest types of such scalar equations, which are natural generalizations of the usual exponential function. 相似文献
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For systems of functional differential equations with nonlinear deviation of argument, we obtain sufficient conditions for the existence of families of their solutions that are continuously differentiable for t R
+. We also investigate the asymptotic behavior of these solutions. 相似文献