共查询到20条相似文献,搜索用时 41 毫秒
1.
Miroslav Bartu
ek 《Journal of Mathematical Analysis and Applications》2003,280(2):232-240
In the paper sufficient conditions are given under which the differential equation y(n)=f(t,y,…,y(n−2))g(y(n−1)) has a singular solution y :[T,τ)→R, τ<∞ fulfilling 相似文献
2.
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
3.
Valeriy A. Yumaguzhin 《Acta Appl Math》2010,109(1):283-313
This paper is devoted to differential invariants of equations
y"=a3(x,y)y¢3+a2(x,y)y¢2+a1(x,y)y¢+a0(x,y).y'=a^{3}(x,y)y^{\prime3}+a^{2}(x,y)y^{\prime2}+a^{1}(x,y)y'+a^{0}(x,y). 相似文献
4.
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
5.
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
6.
A planar mapping was derived from a second order delay differential equation with a piecewise constant argument. Invariant curves for the planar mapping reflects on the dynamics of the differential equation. Results were reported on a planar mapping admitting quadratic invariant curves y=x 2+C, except for the case -3/4≥C≤0. This remaining case is now resolved, and we describe the solutions of the functional equation K(x 2+C)+k(x)=x by iterations of y. 相似文献
7.
8.
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
9.
In this piece of work, we introduce a new idea and obtain stability interval for explicit difference schemes of O(k2+h2) for one, two and three space dimensional second-order hyperbolic equations utt=a(x,t)uxx+α(x,t)ux-2η2(x,t)u,utt=a(x,y,t)uxx+b(x,y,t)uyy+α(x,y,t)ux+β(x,y,t)uy-2η2(x,y,t)u, and utt=a(x,y,z,t)uxx+b(x,y,z,t)uyy+c(x,y,z,t)uzz+α(x,y,z,t)ux+β(x,y,z,t)uy+γ(x,y,z,t)uz-2η2(x,y,z,t)u,0<x,y,z<1,t>0 subject to appropriate initial and Dirichlet boundary conditions, where h>0 and k>0 are grid sizes in space and time coordinates, respectively. A new idea is also introduced to obtain explicit difference schemes of O(k2) in order to obtain numerical solution of u at first time step in a different manner. 相似文献
10.
For x and y vertices of a connected graph G, let TG(x, y) denote the expected time before a random walk starting from x reaches y. We determine, for each n > 0, the n-vertex graph G and vertices x and y for which TG(x, y) is maximized. the extremal graph consists of a clique on ?(2n + 1)/3?) (or ?)(2n ? 2)/3?) vertices, including x, to which a path on the remaining vertices, ending in y, has been attached; the expected time TG(x, y) to reach y from x in this graph is approximately 4n3/27. 相似文献
11.
Vedat Suat Erturk Shaher Momani Zaid Odibat 《Communications in Nonlinear Science & Numerical Simulation》2008,13(8):1642-1654
In a recent paper [Odibat Z, Momani S, Erturk VS. Generalized differential transform method: application to differential equations of fractional order, Appl Math Comput. submitted for publication] the authors presented a new generalization of the differential transform method that would extended the application of the method to differential equations of fractional order. In this paper, an application of the new technique is applied to solve fractional differential equations of the form y(μ)(t)=f(t,y(t),y(β1)(t),y(β2)(t),…,y(βn)(t)) with μ>βn>βn-1>…>β1>0, combined with suitable initial conditions. The fractional derivatives are understood in the Caputo sense. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the new generalization. 相似文献
12.
A new quadratic nonconforming finite element on rectangles (or parallelograms) is introduced. The nonconforming element consists of P2 ⊕ Span{x2y,xy2} on a rectangle and eight degrees of freedom. Our element is essentially of seven degrees of freedom since the degree of freedom associated with the integration on rectangle is essentially of bubble‐function nature. Global basis functions are constructed for both Dirichlet and Neumann type of problems; accordingly the corresponding dimensions are counted. The local and global interpolation operators are defined. Error estimates of optimal order are derived in both broken energy and L2(Ω) norms for second‐order of elliptic problems. Brief numerical results are also shown to confirm the optimality of the presented quadratic nonconforming element. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
13.
We obtain a generalization of the complete Perron effect whereby the characteristic exponents of all solutions change their
sign from negative for the linear approximation system to positive for a nonlinear system with perturbations of higher-order
smallness [Differ. Uravn., 2010, vol. 46, no. 10, pp. 1388–1402]. Namely, for arbitrary parameters λ
1 ≤ λ
2 < 0 and m > 1 and for arbitrary intervals [b
i
, d
i
) ⊂ [λ
i
,+∞), i = 1, 2, with boundaries d
1 ≤ b
2, we prove the existence of (i) a two-dimensional linear differential system with bounded coefficient matrix A(t) infinitely differentiable on the half-line t ≥ 1 and with characteristic exponents λ
1(A) = λ
1 ≤ λ
2(A) = λ
2 < 0; (ii) a perturbation f(t, y) of smallness order m > 1 infinitely differentiable with respect to time t > 1 and continuously differentiable with respect to y
1 and y
2, y = (y
1, y
2) ∈ R
2 such that all nontrivial solutions y(t, c), c ∈ R
2, of the nonlinear system .y = A(t)y + f(t, y), y ∈ R
2, t ≥ 1, are infinitely extendible to the right and have characteristic exponents λ[y] ∈ [b
1, d
1) for c
2 = 0 and λ[y] ∈ [b
2, d
2) for c
2 ≠ 0. 相似文献
14.
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
15.
16.
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
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