共查询到20条相似文献,搜索用时 31 毫秒
1.
Hui-zhao Liu Da-qing Jiang Yan WangDepartment of Applied Mathematics Hebei University of Technology Tianjin ChinaDepartment of Mathematics Northeast Normal University Changchun China 《应用数学学报(英文版)》2002,18(2):249-254
Abstract Positive solutions to the boundary value problem, y'=-f(x,y(w(x)) 0相似文献
2.
William B. Day 《Applied mathematics and computation》1975,1(4):325-331
Estimates of the eigenvalues of the Sturm-Liouville problem —y+q(x)y = λy1y(0) = 0 = y(1) are obtained by making linear approximations of q(x) over subintervals of [0, 1] when q(x) has a bounded second derivative. 相似文献
3.
In this paper we deal with ordinary differential equations of the form dy/dx = P(x, y) where P(x, y) is a real polynomial in the variables x and y, of degree n in the variable y. If y = φ(x) is a solution of this equation defined for x ∈ [0, 1] and which satisfies φ(0) = φ(1), we say that it is a periodic orbit. A limit cycle is an isolated periodic orbit in the set of all periodic orbits. If
φ(x) is a polynomial, then φ(x) is called a polynomial solution. 相似文献
4.
Margherita Fochi 《Aequationes Mathematicae》2009,78(3):309-320
Let X be a real inner product space of dimension greater than 2 and f be a real functional defined on X. Applying some ideas from the recent studies made on the alternative-conditional functional equation
(x, y) = 0 T f(x + y)2 = [f(x) + f(y)]2(x, y) = 0 \Rightarrow f(x + y)^2 = [f(x) + f(y)]^{2} 相似文献
5.
H. S. Witsenhausen 《Journal of Optimization Theory and Applications》1987,54(1):143-155
For variables (x,y,z) in [0, 1]3, three functionsA(y,z),B(z,x),C(x,y), with values in [0, 1], are to be chosen to minimize the integral, over (x,y,z) in the unit cube, ofAB+BC+CA, subject to prescribed values for the integral of each function. It is shown that a minimum can be achieved by dividing each of thex,y,z intervals into three or fewer subintervals and taking each ofA,B,C as indicator function of the union of some of the nine (or fewer) rectangles into which this divides its domain. Several specializations and generalizations of this problem are given consideration. It can be considered as a decision problem with distributed information. 相似文献
6.
Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17] and [19] on interval maps or tree maps. 相似文献
7.
The functional equationf(x,y)+g(x)h(y)F(u/1?x,ν/1?y)=f(u,ν)+g(u)h(ν)F(x/1?u,y/1?ν) ... (1) forx, y, u, ν ∈ [0, 1) andx+u,y+ν ∈ [0,1) whereg andh satisfy the functional equationφ (x+y?xy)=φ(x)φ(y)... (2) has been solved for some non-constant solution of (2) in [0, 1] withφ (0)=1,φ(1)=0 and the solution is used in characterising some measures of information. 相似文献
8.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
Folowing [7], we consider a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ε ∈ ℂ, is said to have a parametric center, if for any ɛ and for any solutiony(ɛ,x) of (**)y(ɛ, 0)≡y(ɛ, 1)..
We give another proof of the fact, shown in [6], that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and generalize a “canonical representation” ofm
k
(x) given in [7]. On this base we prove in some additional cases a composition conjecture, stated in [6, 7] for a parametric
center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
9.
Cihat Abdioğlu 《代数通讯》2017,45(4):1741-1756
Let R be a noncommutative prime ring with extended centroid C and maximal left ring of quotients Qml(R). The aim of the paper is to study a basic functional identity concerning bi-additive maps on R. Precisely, it is proved that a bi-additive map B:R×R→Qml(R) satisfying [B(x,y),[x,y]] = 0 for all x,y∈R must be of the form (x,y)?λ[x,y]+μ(x,y) for x,y∈R, where λ∈C and μ:R×R→C is a bi-additive map. As applications to the theorem, Jordan σ-biderivations with σ an epimorphism and additive commuting maps on noncommutative Lie ideals of R are characterized. 相似文献
10.
We consider optimal control problems for one-dimensional diffusion processes y x (t) = y v x (t), solutions dy x (t) = g(y x (t) dt + σ(y x (t)(dw) + dv t with y x(0) = x& isinv;[a,b], the control processes v t are increasing, positive, and adapted. Several types of expected cost structures associated with each policy v(.) are adopted, e.g. discounted cost, long term average cost and time average cost. Our work is related to [2,6,12,14,16 and 21], where diffusions are allowed to evolve in the whole space, and to [13] and [20], where diffusions evolve only in bounded regions. We shall present some analytic results about value functions, mainly their characterizations, by simple dynamic programming arguments. Several simple examples are explicitly solved to illustrate the singular behaviour of our problems 相似文献
11.
12.
On Hilbert''s Integral Inequality 总被引:5,自引:0,他引:5
In this paper, we generalize Hilbert's integral inequality and its equivalent form by introducing three parameterst,a, andb.Iff, g L2[0, ∞), then[formula]where π is the best value. The inequality (1) is well known as Hilbert's integral inequality, and its equivalent form is[formula]where π2is also the best value (cf. [[1], Chap. 9]). Recently, Hu Ke made the following improvement of (1) by introducing a real functionc(x),[formula]wherek(x) = 2/π∫∞0(c(t2x)/(1 + t2)) dt − c(x), 1 − c(x) + c(y) ≥ 0, andf, g ≥ 0 (cf. [[2]]). In this paper, some generalizations of (1) and (2) are given in the following theorems, which are other than those in [ [2]]. 相似文献
13.
P. Rvsz 《Journal of multivariate analysis》1985,16(3):277-289
{W(x, y), x≥0, y≥0} be a Wiener process and let η(u, (x, y)) be its local time. The continuity of η in (x, y) is investigated, i.e., an upper estimate of the process η(μ, [x, x + α) × [y, y + β)) is given when αβ is small. 相似文献
14.
The nonlinear hyperbolic equation ∂2u(x, y)/∂x ∂y + g(x, y)f(u(x, y)) = 0 with u(x, 0) = φ(x) and u(0, y) = Ψ(y), considered by [1.], 31–45) under appropriate smoothness conditions, is solvable by the author's decomposition method (“Stochastic Systems,” Academic Press, 1983 and “Nonlinear Stochastic Operator Equations,” Academic Press, 1986). 相似文献
15.
Dominik Benkovič 《代数通讯》2018,46(5):1859-1867
For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G. 相似文献
16.
O. A. Shveikina 《Differential Equations》2014,50(5):623-632
We consider the Sturm-Liouville operator L(y) = ?d 2 y/dx 2 + q(x)y in the space L 2[0, π], where the potential q(x) is a complex-valued distribution of the first order of singularity; i.e., q(x) = u′(x), u ∈ L 2[0, π]. (Here the derivative is understood in the sense of distributions.) We obtain asymptotic formulas for the eigenvalues and eigenfunctions of the operator in the case of the Neumann-Dirichlet conditions [y [1](0) = 0, y(π) = 0] and Neumann conditions [y [1](0) = 0, y [1](π) = 0] and refine similar formulas for all types of boundary conditions. The leading and second terms of asymptotics are found in closed form. 相似文献
17.
Dragan Dimitrovski Dragana Radosavljevi? Miloje Rajovi? Rade Stoiljkovi? 《Acta Mathematica Hungarica》2011,132(1-2):15-26
It is shown that Sturm theorems, formulated in the 1830??s ([1], [2], [3] and [4]) and valid for second order linear homogeneous differential equation L(y)??y??+a(x)y??+b(x)y=0, could as well be formulated for the class of nonhomogeneous linear differential equations L(y)=f(x). Criteria for the existence of oscillatory solutions of nonhomogeneous equations, as well as more exact locations of the zeros are given. 相似文献
18.
Yu. K. Sabitova 《Russian Mathematics (Iz VUZ)》2009,53(12):41-49
We consider the equation y
m
u
xx
− u
yy
− b
2
y
m
u = 0 in the rectangular area {(x, y) | 0 < x < 1, 0 < y < T}, where m < 0, b ≥ 0, T > 0 are given real numbers. For this equation we study problems with initial conditions u(x, 0) = τ(x), u
y
(x, 0) = ν(x), 0 ≤ x ≤ 1, and nonlocal boundary conditions u(0, y) = u(1, y), u
x
(0, y) = 0 or u
x
(0, y) = u
x
(1, y), u(1, y) = 0 with 0≤y≤T. Using the method of spectral analysis, we prove the uniqueness and existence theorems for solutions to these problems 相似文献
19.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
We introduce a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ℂ, is said to have a parametric center, if for any ε and for any solutiony(ε,x) of (**),y(ε,0)≡y(ε,1).
We show that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and on this base prove in some special cases a composition conjecture, stated in [10], for a parametric center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
20.
Let R be a reduced commutative ring with 1 ≠ 0. Let R E be the set of equivalence classes for the equivalence relation on R given by x ~ y if and only if ann R (x) = ann R (y). Then R E is a (meet) semilattice with respect to the order [x] ≤ [y] if and only if ann R (y) ? ann R (x). In this paper, we investigate when R E is a lattice and relate this to when R is weakly complemented or satisfies the annihilator condition. We also consider when R is a (meet) semilattice with respect to the Abian order defined by x ≤ y if and only if xy = x 2. 相似文献
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