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1.
Global Existence of Positive
Periodic Solutions for a Distributed Delay Competition Model 总被引:3,自引:0,他引:3
Xian-yi Li De-ming ZhuDepartment of Mathematics East China Normal University Shanghai China Department of Mathematics Physics Nanhua University Hengyang China 《应用数学学报(英文版)》2003,19(3):491-498
By using the continuation theorem of Mawhin's coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition modelwhere ri and r2 are continuous w-periodic functions in R+=[0,∞) with ,ai,ci(i =1,2) are positive continuous w-periodic functions in R+=[0,∞),bi (i = 1,2) is nonnegative continuous w-periodic function in R+=[0,∞), w and T are positive constants. Ki,Lt ∈ C([-T,0], (01 88)) and Ki(s)ds = 1,ds - 1. i = 1,2. Some known results are improved and extended. 相似文献
2.
Shi Ping LU Wei Gao GE 《数学学报(英文版)》2005,21(6):1309-1314
Thc main aim of this paper is to use the continuation theorem of coincidence degree theory for studying the existence of periodic solutions to a kind of neutral functional differential equation as follows:(x(t)-^n∑i=1cix(t-ri))″=f(x(t))x′+g(x(t-τ))+p(t).In order to do so, we analyze the structure of the linear difference operator A : C2π→C2π, [Ax](t) =x(t)-∑^ni=1cix(t-ri)to determine some flmdamental properties first, which we are going to use throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating a priori bounds of periodie solutions. 相似文献
3.
Qi Kang RAN 《数学学报(英文版)》2005,21(4):705-714
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function. 相似文献
4.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
5.
De-xiang Ma Wei-gao Ge Xue-gang Chen 《应用数学学报(英文版)》2005,21(4):661-670
In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{( φp(u'))'+q(t)f(t,u,u')=0,0〈t〈1,u(0)=∑i=1^nαiu(ξi),u'(1)=∑i=1^nβiu'(ξi),whereφp(s)=|s|^p-2s,p≥2;ξi∈(0,1)(i=1,2,…,n),0≤αi,βi〈1(i=1,2,…n),0≤∑i=1^nαi,∑i=1^nβi〈1,and q(t) may be singular at t=0,1,f(t,u,u')may be singular at u'=0 相似文献
6.
On Well-posed Mutually Nearest and
Mutually Furthest Point Problems in Banach Spaces 总被引:3,自引:0,他引:3
ChongLI RenXingNI 《数学学报(英文版)》2004,20(1):147-156
Let G be a non-empty closed(resp.bounded closed)boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X.Let K(X)denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance.Moreover,let KG(X)denote the closure of the set {A∈K(x):A∩G=0}.We prove that the set of all A∈KG(X)(resp.A∈K(X)),such that the minimization (resp.maximization)problem min(A,G)(resp.max(A,G))is well posed,contains a dense Gδ-subset of KG(X)(resp.K(X)).thus extending the recent results due to Blasi,Myjak and Papini and Li. 相似文献
7.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
*Supported by the Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. 20060237 and 20050494). 相似文献
8.
Multilinear Singular Integrals with Rough Kernel 总被引:9,自引:0,他引:9
ShanZhenLU HuoXiongWU PuZHANG 《数学学报(英文版)》2003,19(1):51-62
For a class of multilinear singular integral operators T
A
,
where R
m
(A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m − 1 in
is homogeneous of degree zero, the authors prove that T
A
is bounded from L
p
(ℝ
n
) to
and from L
1(ℝ
n
) to L
n/(n−β),∞(ℝ
n
) with the bound
And if Ω has vanishing moments of order m − 1 and satisfies some kinds of Dini regularity otherwise, then T
A
is also bounded from L
p
(ℝ
n
) to
with the bound
Supported by the National 973 Project (G1990751) and SEDF of China (20010027002) 相似文献
9.
Konrad Gröger Lutz Recke 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(3):263-285
This paper concerns boundary value problems for quasilinear second order elliptic systems which are, for example, of the type
Here Ω is a Lipschitz domain in
νj are the components of the unit outward normal vector field on ∂Ω, the sets Γβ are open in ∂Ω and their relative boundaries are Lipschitz hypersurfaces in ∂Ω. The coefficient functions are supposed to
be bounded and measurable with respect to the space variable and smooth with respect to the unknown vector function u and to the control parameter λ. It is shown that, under natural conditions, such boundary value problems generate smooth
Fredholm maps between appropriate Sobolev-Campanato spaces, that the weak solutions are H?lder continuous up to the boundary
and that the Implicit Function Theorem and the Newton Iteration Procedure are applicable. 相似文献
10.
O. E. Korkuna 《Ukrainian Mathematical Journal》2008,60(5):671-691
We establish conditions for the existence and uniqueness of a generalized solution of the Cauchy problem for the equation
in a Tikhonov-type class.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 586–602, May, 2008. 相似文献
11.
Huaning Liu 《Bulletin of the Brazilian Mathematical Society》2007,38(2):179-188
For integers a,
b and n
> 0, define
and
where
denotes the summation over all
r such that (r, n) = 1, and
is defined by the equation
. The two sums are analogous to the
homogeneous Dedekind sum S(a,b,
n). The functional equations for
A
Γ and B
Γ are established. Furthermore, Knopp's
identity on Dedekind sum is extended.
*This work is supported by the N.S.F. (10271093,
60472068) of P.R. China. 相似文献
12.
S. BERHANU F. CUCCU G. PORRU 《数学学报(英文版)》2007,23(3):479-486
For γ≥1 we consider the solution u=u(x) of the Dirichlet boundary value problem Δu + u^-γ=0 in Ω, u=0 on δΩ. For γ= 1 we find the estimate
u(x)=p(δ(x))[1+A(x)(log 1/δ(x)^-6],
where p(r) ≈ r r√2 log(1/r) near r = 0,δ(x) denotes the distance from x to δΩ, 0 〈ε 〈 1/2, and A(x) is a bounded function. For 1 〈 γ 〈 3 we find
u(x)=(γ+1/√2(γ-1)δ(x))^2/γ+[1+A(x)(δ(x))2γ-1/γ+1]
For γ3= we prove that
u(x)=(2δ(x))^1/2[1+A(x)δ(x)log 1/δ(x)] 相似文献
13.
J. A. López Molina M. E. Puerta M. J. Rivera 《Bulletin of the Brazilian Mathematical Society》2006,37(2):191-216
Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. 相似文献
14.
RenZiYANG JunXiangXU 《数学学报(英文版)》2004,20(3):525-532
In this paper we consider the effective reducibility of the following linear differentialequation: x = (A ∈Q(t,∈))x, |∈| ≤ ∈0, where A is a constant matrix, Q(t,e) is quasiperiodic in t, and e is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to y = (A^*(∈) R^*(t, ∈))y, |∈| ≤ ∈o, where R^* is exponentially small in ∈. 相似文献
15.
E.M.E.ZAYED 《数学学报(英文版)》2004,20(2):209-222
The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. 相似文献
16.
MingXiong 《应用数学学报(英文版)》2004,20(4):665-674
Some results concerning existence of positive solutions for the singular boundary value problems u^(4)(t)=f(t,u(t)) t∈(0,1) u(0)=u(1)=0 u‘(0)=u‘(1)=0 have been given, where f(t, x) may be singular at t = 0, 1. 相似文献
17.
Zhi-ting Xu 《应用数学学报(英文版)》2007,23(4):569-578
Some oscillation theorems are given for the nonlinear second order elliptic equationsum from i,j=1 to N D_i[a_(ij)(x)Ψ(y)||▽y||~(p-2)D_(jy)] c(x)f(y)=0.The results are extensions of modified Riccati techniques and include recent results of Usami. 相似文献
18.
A theorem from the classical complex analysis proved by Davydov in 1949 is extended to the theory of solution of a special
case of the Beltrami equation in the z-complex plane (i.e., null solutions of the differential operator ).
It is proved that if γ is a rectifiable Jordan closed curve and f is a continuous complex-valued function on γ such that the integral
converges uniformly on γ as r → 0, where n(ζ) is the unit vector of outer normal on γ at a point ζ and ds is the differential of arc length, then the β-Cauchy-type integral
admits a continuous extension to γ and a version of the Sokhotski–Plemelj formulas holds.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1443–1448, November, 2008. 相似文献
19.
Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:
where (λ
n
) is a sequence of positive steps. Algorithm may be viewed as the discretized equation of a nonlinear oscillator subject to friction. We prove that, if 0 ∈ int (A(0)) (condition of dry friction), then the sequence (x
n
) generated by is strongly convergent and its limit x
∞ satisfies 0 ∈ A(0) + B(x
∞). We show that, under a general condition, the limit x
∞ is achieved in a finite number of iterations. When this condition is not satisfied, we prove in a rather large setting that
the convergence rate is at least geometrical. 相似文献
20.
Nicolae Popescu Marian Vâjâitu Alexandru Zaharescu 《Algebras and Representation Theory》2006,9(1):47-66
Let T be a transcendental element of
and
the orbit of T. On
we have a Haar measure
. The goal of this paper is to characterize all the elements of
for which the integral
, called the trace of T, is well defined.Presented by A. Verschoren 相似文献