共查询到20条相似文献,搜索用时 15 毫秒
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I. N. Sergeev 《Moscow University Mathematics Bulletin》2009,64(3):113-120
Both global attainability and global reducibility problems for a controllable system equivalent to a linear differential equation are positively solved. Furthermore, the existence of a linear equation having a given Cauchy matrix on a given segment and coinciding with given equations from the left and right of that segment is proved. The results obtained allow one to construct a linear equation with the fundamental solutions system possessing preassigned properties. 相似文献
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In this paper, we consider a logistic delay equation with a linear delay harvesting term of the following form:in both cases when and . We present some results on the boundedness and positiveness of the solutions of this equation without the condition that is upper bounded by some constant which is necessary to the corresponding results in [L. Berezansky, E. Braverman, L. Idels, Delay differential logistic equation with harvesting, Math. Comput. Modelling 40 (2004) 1509–1525], and our results extend these known results. 相似文献
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Richard E. Ewing 《Journal of Mathematical Analysis and Applications》1979,71(1):167-186
Numerical approximation of the solution of the Cauchy problem for the linear parabolic partial differential equation is considered. The problem: (p(x)ux)x ? q(x)u = p(x)ut, 0 < x < 1,0 < t? T; ; ; p(0) ux(0, t) = g(t), 0 < t0 ? t ? T, is ill-posed in the sense of Hadamard. Complex variable and Dirichlet series techniques are used to establish Hölder continuous dependence of the solution upon the data under the additional assumption of a known uniform bound for ¦ u(x, t)¦ when 0 ? x ? 1 and 0 ? t ? T. Numerical results are obtained for the problem where the data ?1, ?2 and g are known only approximately. 相似文献
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I. M. Plaksina 《Russian Mathematics (Iz VUZ)》2013,57(10):13-18
We study first-order functional differential equations which are singular in the independent variable, establish criteria for the constant sign property of the Cauchy function, and prove an assertion analogous to the Vallée-Poussin theorem. 相似文献
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G. Gripenberg S.-O. Londen J. Prüss 《Mathematical Methods in the Applied Sciences》1997,20(16):1427-1448
It is proved that there is a (weak) solution of the equation ut=a*uxx+b*g(ux)x+f, on ℝ+ (where * denotes convolution over (−∞, t)) such that ux is locally bounded. Emphasis is put on having the assumptions on the initial conditions as weak as possible. The kernels a and b are completely monotone and if a(t)=t−α, b(t)=t−β, and g(ξ)∼sign(ξ)∣ξ∣γ for large ξ, then the main assumption is that α>(2γ+2)/(3γ+1)β+(2γ−2)/(3γ+1). © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
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Necessary conditions for the optimal control of a linear system of neutral type functional differential equations are obtained. We show that a success in reducing the initial problem to the problem of solvability of a certain boundary value problem is, in principle, a question of one's ability to construct adjoint operators to the operators appearing in the initial control problem. 相似文献
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We develop a theory of “special functions” associated with a certain fourth-order differential operator Dm,n\mathcal{D}_{\mu,\nu} on ℝ depending on two parameters μ,ν. For integers μ,ν≥−1 with μ+ν∈2ℕ0, this operator extends to a self-adjoint operator on L
2(ℝ+,x
μ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive
basic properties of the eigenfunctions such as orthogonality, completeness, L
2-norms, integral representations, and various recurrence relations. 相似文献
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B. Stankovi? 《Journal of Mathematical Analysis and Applications》2006,324(2):1462-1469
In this paper we construct generalized solutions (weak solutions) to a linear discontinuous differential equation which appears as mathematical model in mechanics and for which usual methods are not quite adequate. The result is applied to the equation of an elastic beam on a Winkler type of foundation. 相似文献
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《Statistics & probability letters》1987,5(3):231-234
In this note we study the properties of the solution of a two-parameter linear stochastic differential equation with constant coefficients. We prove, in particular, that this solution may be negative with positive probability. 相似文献
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A method for constructing the Green's function for a differential equation with a deviating argument is proposed, and the boundary-value problemx'(t)+p (t) (t) x (h (t)) = f (t), t [a, b], x(a) = x(b) = 0 is used as an example. The method increases the possibilities for construction of Green's functions compared to the present methods, including the possibilities for representation of the Green's function in terms of the Cauchy function.Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 443–448, March, 1975. 相似文献
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Perturbation bounds are given for the solution of the nth order differential matrix Riccati equation using the associated linear 2nth order differential system. The new bounds are alternative to those existing in the literature and are sharper in some cases.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Xia Gao 《Journal of Number Theory》2011,131(6):994-1019
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The goal of this note is to generalize a formula of Datskovsky and Wright on the zeta function associated with integral binary cubic forms. We show that for a fixed number field K of degree d, the zeta function associated with decomposable forms belonging to K in d−1 variables can be factored into a product of Riemann and Dedekind zeta functions in a similar fashion. We establish a one-to-one correspondence between the pure module classes of rank d−1 of K and the integral ideals of width <d−1. This reduces the problem to counting integral ideals of a special type, which can be solved using a tailored Moebius inversion argument. As a by-product, we obtain a characterization of the conductor ideals for orders of number fields.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=RePyaF8vDnE. 相似文献19.
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John A.D. Appleby 《Journal of Mathematical Analysis and Applications》2011,380(2):814-830
In this paper we consider a linear stochastic Volterra equation which has a stationary solution. We show that when the kernel of the fundamental solution is regularly varying at infinity with a log-convex tail integral, then the autocovariance function of the stationary solution is also regularly varying at infinity and its exact pointwise rate of decay can be determined. Moreover, it can be shown that this stationary process has either long memory in the sense that the autocovariance function is not integrable over the reals or is subexponential. Under certain conditions upon the kernel, even arbitrarily slow decay rates of the autocovariance function can be achieved. Analogous results are obtained for the corresponding discrete equation. 相似文献