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1.
1 IntroductionIn this paper we deal with the oscilIatory behaviour of solutions of nonlinear third orderdifferential equations of tlie formandwhere pt q E C([a,co),R) la E R, f E C(R,R) such that ap 3 g > 0 for V / 0 and 7 > 0 isa quotient of odd integers.By a proper solutiOn of (1) or (2) we mean a solution y of the equation which exi8ts on somehalf line [Tg, oo) 5 [a, oo), where Tv depens on y, and is llontirivial in some neighbourhood ofinfinity that is y(t) / 0 in [t., oo) fOr some t…  相似文献   

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1. IntroductionWienerHopf equations are integral equations defined on the haif line:where rr > 0, a(.) C L1(ro and g(.) E L2(at). Here R = (--oo,oo) and ty [0,oo). Inou-r discussions, we assume that a(.) is colljugate symmetric, i.e. a(--t) = a(t). WienerHop f equations arise in a variety of practical aPplicatiolls in mathematics and ellgineering, forinstance, in the linear prediction problems fOr stationary stochastic processes [8, pp.145--146],diffuSion problems and scattering problems […  相似文献   

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Let X be a metric space andμa finite Borel measure on X. Let pμq,t and pμq,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge (μB(x,r))q(2r)t, where q, t∈R. For any compact set E of finite packing premeasure the authors prove: (1) if q≤0 then pμq,t(E)=pμq,t(E);(2)if q>0 andμis doubling on E then pμq,t(E) and pμq,t(E) are both zero or neither.  相似文献   

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1 IntroductionIn recent years) there were many results of studying boundary value problemsfor functional differential equations [1-5]. But the boundary conditions are allDirichlet's type. In this paper, we will study a kind of boundary value problemswitb integro boundary condition fOr the functional differential equdtionswhere f(t, yt, x, y) is a continuous real function defined on the set fl = [0, T] xC. x R', and is continuously differentiable with respect to each variable x, y;p E C. = C…  相似文献   

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1 IntroductionConsider the red blood ceels growth model with several delayswhere r(t) E C([0, oo), (0, oo)), Pil ri) n e (0, oo), and r1 2 r2 2'' 2 rm.Eq.(l) was used first by Wazewska-Czyzewska and Lasota [l] as a model forthe survival of the red blood ceels in an animal, see also Arino and Kimmel[2]. There are a lot of activities concerning the asymptotic behavior of (1),see for examp1e [3] and the references cited therein. The following results wasobtained in [l, 3, 4].N'(t) = --pN(t)…  相似文献   

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Let L^2([0, 1], x) be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2([0, 1], x) defined by a linear combination of Jo(μkX), where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2([0, 1], x), let E(f, n) be the error of the best L2([0, 1], x), i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T(t)f(x)=1/π∫0^π f(√x^2 +t^2-2xtcosO)dθ The differences (I- T(t))^r/2f = ∑j=0^∞(-1)^j(j^r/2)T^j(t)f of order r ∈ (0, ∞) and the L^2([0, 1],x)- modulus of continuity ωr(f,τ) = sup{||(I- T(t))^r/2f||:0≤ t ≤τ] of order r are defined in the standard way, where T^0(t) = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E(f, n) and ωr(f, τ) for some cases of r and τ. More precisely, we will find the smallest constant n(τ, r) which depends only on n, r, and % such that the inequality E(f, n)≤ n(τ, r)ωr(f, τ) is valid.  相似文献   

7.
A regular semigroup S with a special involution *, i.e., a unary operation on S satisfyingis called a regular *-semigroup[1]. It has been shown by Yamada[2] that a regular semigroup S isa regular *-semigroup if and only if it has a P-system, that is to say, there is a subset P of E(S)such that(2) As a generalization of regular semigroup and orthodox semigroup,Yamada[3] defined P-regular semigroup. Let S be a regularsemigroup. A subset P of E(S) is called a C-set in S if(c.2) (1) In this…  相似文献   

8.
1 IntroductionAs we know, any given quadratic system which may have limit cycle (LC,fOr abbreviation) can be written in the fOllowing fOrm (see [1] 512)where 6, l, m, n, a, 6 are all real parameters.If all trajectories of a quadratic system remain bounded fOr t 2 0, we saythat the system is bounded, and fOr abbreviation denote by BQS in this paper.The research work for BQS begin with Dickson-Perko [3]. And then, in [4],they made use of the conclusions of [51 to give a detailed classifica…  相似文献   

9.
The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) > 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.  相似文献   

10.
§ 1 IntroductionConsider the difference equationΔyn=rnynK -yn- ln K -cyn- ln,  n =0 ,1 ,2 ,...,( 1 .1 )whereΔ is the forward difference operator defined byΔyn=yn+1 -yn,{rn}n≥ 0 is a sequenceof nonnegative real numbers,{ln}n≥ 0 is a sequence of positive integers,{n-ln}n≥ 0 is nonde-creasing,limn→∞ ( n-ln) =∞ ,and K is a positive constant,c∈ [0 ,1 ) .Obviously,( 1 .1 ) is aformally discrete analogue of the following single population growth model:N′( t) =r( t) N( t) K -N( t-τ( t…  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.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

15.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  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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