共查询到19条相似文献,搜索用时 62 毫秒
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研究一类非线性无界时滞差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了有关的结果。 相似文献
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本文研究一类高阶非线性双曲型方程utt-uxx+μuxxx-αuxxtt+βuxxxxtt=f(ux)x的Cauchy问题,证明问题解的存在性与唯一性,并给出解在有限时刻爆破的充分条件. 相似文献
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研究一类非线性高阶中立型差分方程的振动性,给出了该方程振动的几个充分条件,改进,扩展了[4]的有关结果。 相似文献
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讨论具强迫项高阶非线性中立型差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=fn,n=0,1,2,…及其相关联的差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=0,n=0,1,2,…的振动性与渐近性,得到了所有解振动或趋于零的充分性判据. 相似文献
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本文利用Banach不动点定理证明一类非线性发展方程的非局部Cauchy问题解的存在性与唯一性,及其对非局部拟线性抛物方程的应用。 相似文献
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关于微分差分方程组周期解的存在性 总被引:5,自引:0,他引:5
目前,对泛函微分方程周期解的存在性问题的研究,主要用不动点原理这个工具,这种方法可用丁证明周期解的存在,但较少涉及周期解的个数与周期。本文采用了一种构造性方法去研究微分差分方程组周期解的存在性,这种方法是由Kaplan与Yorke所引入,井被温立志改进了的,原来被用于研究标量方程,在本文中,首次将它用于研究方程组, 相似文献
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关于一类非线性发展方程整体解的存在性问题 总被引:15,自引:1,他引:15
本文研究一类模拟非线性弹性杆的纵振动的非线性发展方程的初边值问题,证明了其整体解的存在性、唯一性、光滑性及在一定条件下,整体解的不存在性。 相似文献
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ConsiderneutraldifferentialdiffereflceequatinwhereTE(0,co),ae[0,co),Q(t)EC[[t.,co),R ].In1988,G.Ladaspresentedanopenprobleminprivatecommuni(:ationandthenin[1].Theproblemisasfollowing:Assumethatfi:Q(s)ds=co,showthateverynonoscillatorysollltioTIot'equation(… 相似文献
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一类四阶非线性方程奇摄动边值问题解的估计 总被引:1,自引:0,他引:1
本文考虑了一类四阶非线性方程边值问题的奇摄动,在适当的条件下,构造了其渐近展开式,证明了解的存在性及高阶一致有效渐近估计。 相似文献
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REGULARIZATION OF AN ILL-POSED HYPERBOLIC PROBLEM AND THE UNIQUENESS OF THE SOLUTION BY A WAVELET GALERKIN METHOD 下载免费PDF全文
We consider the problem K(x)u xx = u tt , 0 < x < 1, t ≥ 0, with the boundary condition u(0,t) = g(t) ∈ L 2 (R) and u x (0, t ) = 0, where K(x) is continuous and 0 < α≤ K (x) < +∞. This is an ill-posed problem in the sense that, if the solution exists, it does not depend continuously on g. Considering the existence of a solution u(x, ) ∈ H 2 (R) and using a wavelet Galerkin method with Meyer multiresolution analysis, we regularize the ill-posedness of the problem. Furthermore we prove the uniqueness of the solution for this problem. 相似文献
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本文研究了三维Laplace方程的柯西问题.该问题是不适定的,即其解(若存在)不连续依赖原始数据.利用Meyer小波和小波Galerkin方法,获得了在L2范数意义下的稳定小波逼近解,并且给出分辨率水平的选取方法. 相似文献
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刘健 《数学物理学报(B辑英文版)》2012,(4):1298-1320
This paper is concerned with the free boundary value problem for multidimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. Local (in time) existence of a weak solution is established; in particular, the density is positive and the solution is regular away from the free boundary. 相似文献
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We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna & Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem. 相似文献