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1.
该文利用Krasnoselskii不动点定理和Schwarz不等式, 获得了关于非自治的广义单种群Logistic模型 x=x(t){a(t)-b(t)x(t)-∑ni=1ci (t)x(t-τi(t))-∫0-∞k(t, s)x(t+s)ds} 的正周期解的存在性和唯一性的一些新的结果.  相似文献   

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主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.  相似文献   

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对于非线性抛物型方程其中QT=Ω×(0,T)是上半空间R+n+1中的一个柱形区域,ST=Ω×[0,T]是Q_T的侧面,Ω是R~n中的一个有界区域,其边界Ω充分光滑,本文着重讨论函数ai(x,t,u,s)和a(x,t,u,s)关于变元s=(s1…,sn)按指数形式快速增长的情形.文中得到了强非线性抛物型方程(1.1)和(1.2)在空间中广义解的存在性.这个结果也包括了ai(x,t,u,s)及a(x,t,u,s)关于变元s=(s1..,sn)按幂次|s|n的形式增长的情形,改正了Ladyenskaja等的文献中第五章定理6.7的证明中的一个疏忽。  相似文献   

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冯敬海  沙震 《中国科学A辑》1997,40(12):1096-1100
设随机过程x(t)(t∈[0,∞))是一个从属过程,X[0,1]=|x∈R:t∈[0,1],X(t)=x}.通过对x(t)的指标函数g(u)(u≥0)的细致分析得到了关于X[0,1]填充测度函数的判别准则.事实上,若φ(s)(s∈(0,1))为任一测度函数,记h(s)=φ(s)/g(1/s),则有:h-p(x|0,1|= 相应于∫10φ2(s)/s ds{<+∞ =+∞  相似文献   

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In this paper we study the oscillation of the retarded differential equation x′(t)+∫abp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (1)and the advanced differential equation x′(t)-∫abp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (2) We improved the main results of [1-4].  相似文献   

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本文考虑Banach空间是形如x(t)=u(t)+∫Gtf(t,s,x(s))ds的广义Volterra积分方程,利用M?nch不动点定理得到所论方程解的某些存在定理.  相似文献   

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该文运用锥上的不动点定理研究非线性二阶常微分方程无穷多点边值问题 u'+a (t ) f (u)=0, t∈(0, 1), u(0)=0, u(1)=∑i =1α i u ( ξ i ) 正解的存在性. 其中ξ i∈ (0,1),α i∈ [0,∞), 且满足∑i=1αiξ i <1.α∈C([0,1], [0,)),f∈C ([0,∞), [0,∞)).  相似文献   

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Theorem. A mapping x** of X* into sealar field Φ is a linear functional if and only if there exists a μ∈ba(S) such that X**(X*)=∫sx*(s)μ(ds),x*∈X* Theorem. F∈ba(S.Σ)* if and only if there exists a λ∈ba (T) (T is the closed unit sphere of the space B(S,Σ))such that F(μ)=∫(∫st(s)μ(ds))λ(dt),μ∈ba(S,Σ).  相似文献   

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研究了一种新型不连续函数的积分不等式um(t)≤φ(t)+m-m n∫tt0f(s)un(s)w(u(s))ds+t0∑相似文献   

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在本世纪初,T.H.Gronwall[1]建立了基本不等式如下:a(t),u(t)为[0,T]上非负连续函数,k 为非负常数,则由u(t)≤k+(?)a(s)u(s)ds,t∈[0,T]可以推出不等式u(t)≤kexp((?)a(s)ds),t∈[0,T].1956年,I.Bihari[2]得到推广的结果如下:  相似文献   

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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

14.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

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<正>Aims and Scope Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,is one of the transactions of China Society for Industrial and Applied Mathematics,and is a bimonthly journal.JMRA is dedicated to publishing first-rate original research papers in all areas of mathematics with applications,and making research findings available to a wide scientific world,as JMRE has for many years.In line with the name change,the new scope of Journal of Mathematical Research with Applications will not include the articles on mathematical methodology and mathematical philosophy.Copyright Information  相似文献   

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<正>Erratum to:Science in China Series A:Mathematics,April 2009 Vol.52 No.4:617–630doi:10.1007/s11425-009-0038-2There is a mistake in the proof of[1,Lemma 2.2],which occurs in 4-th line at[1,p.619],  相似文献   

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<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.  相似文献   

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