共查询到20条相似文献,搜索用时 46 毫秒
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本文证明了拟线性退化抛物方程 (e)u/(e)t=n∑i=1 (e)/(e)xi(aij(u)(e)u/(e)xi)+n∑i=1 (e)bi(u)/(e)xi -c(u), u(x,0)=u0(x),aij(u)ξiξj≥0,(A)ξ∈Rn 的Cauchy问题BV解的唯一性和稳定性. 相似文献
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应用整体反函数理论证明了广义L ienard方程a(t)x" f(x,x′)x′ g(t,x)=e(t),x(0)-x(2π)=x(′0)-x′(2π)=0,周期解的存在唯一性,并由此得到它在几种特殊情况下周期解的存在唯一性定理. 相似文献
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考虑具连续时滞和离散时滞的中立型积分微分方程d/dt[x(t) q∑j=1ej(t)x(t-δj(t))]=A(t,x(t))x(t ∫t-∞ C(t,s)x(s)ds 1∑i=1gi(t,x(t-Υi(t))) b(t)和d/dt[x(t) q∑j=1ej(t)x(t-δj(t))]=A(t)x(t) ∫t-∞C(t,s)x(s)ds 1∑j=1gi(t,x(t-Υi(t))) b(t)周期解的存在性和唯一性问题,利用线性系统指数型二分性理论和泛函分析方法,并通过技巧性代换获得了保证中立型系统周期解存在性和唯一性的充分性条件,从而避开了在研究中立型系统时x(t-δ)时滞项的导数x1(t-δ)的出现,推广了相关文献的主要结果. 相似文献
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考虑具连续时滞和离散时滞的中立型脉冲积分微分方程去{d/dt[x(t)+q∑j=1ej(t)x(t-δj(t))]=A(t,x(t))x(t)+t∫-∞C(t,s)x(s)ds+p∑j=1gj(t,x(t=Ti(t)))+b(t),t≠tk,tktk+1,△x(t)=Bkx(t)+Ik(x(t))+γk,.t=tk,k∈Z.概周期解的存在性和唯一性问题.利用线性系统指数二分性理论和不动点定理,莸得了保证中立型系统概周期解存在性和唯一性的充分条件,推广了相关文献的主要结果. 相似文献
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针对双曲型方程定解问题{utt=a2uxx+f(t),0xπ,a∈R且a≠0,u(0,t)=v1(t),u(π,t)=v2(t),t0,u(x,0)=g(x),ut(x,0)=h(x),0≤x≤π研究了可以唯一决定未知函数组{v1(t),v2(t),f(t)}的基本条件,提出了该定解问题的反问题,并且讨论了此反问题的存在性与唯一性. 相似文献
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一类非线性边值问题K—NODE解的唯一性 总被引:1,自引:0,他引:1
本文在一定条件下给出了(0,+∝)上的非线性边值问题1/(p(t))(p(t)u'(t))'=f(u),t∈(0,+∝),u'(0)=0,u(t)=0,的 k-node 解的唯一性结果(k∈N ∪{0}),其中 f(u)=u(α-f_1(u)),α>0,f_1(u)∈C~1(-∝,+∝)是偶函数。且当 u>0时,f′_1(u)>0,p(t)∈O_2(0,+∝),(p'(t))/(p(t))≥0,且(p')~2-p″p≤0 相似文献
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§1 引言 1974年F.Treves发现重特征方程■以t=0为支柱的Cauchy问题解的唯一性中的“离散现象”(即解唯一的充要条件是p≠1,3,5…),引起许多学者的兴趣。之后,人们以不同的方法从不同角度研究了方程(1) 相似文献
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邓引斌 《数学物理学报(A辑)》1992,12(2):140-149
本文主要讨论了R~n中超线性椭圆方程边值问题的k-node解的唯一性,在条件 p1(n)<-(ι+2)/(p-1)1,同时给出了 -△u+a(|x|)u=sum from t=1 to m a_i(|x|)|u|p~(i-1)u,u→0 (|x|→∞)的k-node解的唯一性结果。 相似文献
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利用Fouier级数理论和不动点原理研究下列方程:d^n/dt^n(x(t)-cs(t-τ))=n/∑/j=1ajx^(n-j)(t) n/∑/j=1bjx(n-j)t-τ) f(t,xt,x′t,…,x^(n-1)t)的周期解问题,得到了解的存在性和唯一性。 相似文献
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We prove existence and uniqueness results for weak solutions of
nonlinear degenerate problems arising in various physical models. The main
novelty in the article concerns the uniqueness, which employs a technique
based in showing that weak solutions are also entropy solutions, for which
uniqueness follows from a straightforward adaptation of known results. We
treat equations with lower order terms that have a particular structure and
show with a counterexample that for general lower order terms the uniqueness
does not hold.AMS Subject Classification: 35D99, 35K65, 35R35. 相似文献
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Guoguang LIN Department of Mathematics Yunnan University Kunming China e-mail: gglin@ynu. edu. cn 《Communications in Nonlinear Science & Numerical Simulation》2000,5(1)
1 FormulationLet fi be a bounded set of R", n 2 2, tv'ith a sufficiently smooth boundary off. ac'e considerthe motion of an incompressible, viscous fluid in fi, which is described by the following systemll]with the initial conditionand the Dirichlet boundary conditionwhere v = (yi, .". u.) is the velocity, p is the pressure, the tensor r = (n j) is defined asp is a. positive constant. Notice that when p = 2 the s}l'steln (1), (2), (5) turns to the N*avierStokes system.A scalar potential to t… 相似文献
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In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case. 相似文献
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Sandrine Dubois 《Journal of Differential Equations》2003,189(1):99-147
We exhibit simple sufficient conditions which give weak-strong uniqueness for the 3D Navier-Stokes equations. The main tools are trilinear estimates and energy inequalities. We then apply our result to the framework of Lorentz, Morrey and Besov over Morrey spaces so as to get new weak-strong uniqueness classes and so uniqueness classes for solutions in the Leray-Hopf class. In the last section, we give a uniqueness and regularity result. We obtain new uniqueness classes for solutions in the Leray-Hopf class without energy inequalities but sufficiently regular. 相似文献
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对于无限时滞泛函微分方程,利用Liapunov泛函的方法,研究了方程概周期解的存在性、唯一性问题,得到了便于应用的概周期解的存在性、唯一性判据. 相似文献
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运用Hodge分解方法,选择适当的检验函数,证明了一类散度形式椭圆型偏微分方程在grand Sobolev空间很弱解的唯一性. 相似文献