共查询到20条相似文献，搜索用时 46 毫秒
1.
We study the expansion of derivatives along orbits of real and complex one-dimensional mapsf, whose Julia setJ
f attracts a finite setCrit of non-flat critical points. Assuming that for eachcεCrit, either |D f
n(f(c))|→∞ (iff is real) orb
n·|Df
n(f(c))|→∞ for some summable sequence {b
n} (iff is complex; this is equivalent to summability of |D f
n(f(c))|−1), we show that for everyxεJ
f\U
i
f
−i(Crit), there existℓ(x)≤max
c
ℓ(c) andK′(x)>0
for infinitely manyn. Here 0=n
s<…<n
1<n
0=n are so-called critical times,c
i is a point inCrit (or a repelling periodic point in the boundary of the immediate basin of a hyperbolic periodic attractor), which shadows
orb(x) forn
i−ni
+1 iterates, and
, for uniform constantsK>0 and λ>1. If allcεCrit have the same critical order, thenK′(x) is uniformly bounded away from 0. Several corollaries are derived. In the complex case, eitherJ
f=
orJ
f has zero Lebesgue measure. Also (assuming all critical points have the same order) there existk>0 such that ifn is the smallest integer such thatx enters a certain critical neighbourhood, then |Df
n(x)|≥k.
The original paper used an incorrect version of the Koebe Lemma cited from [21] as was pointed out by the referee and Genadi
Levin in the autumn of 2001. The corrected version of November 2001 only uses the classical Koebe Lemma. Apparently, all results
in Feliks Przytycki’s paper [21] go through using the classical Koebe Lemma instead of his Lemma 1.2.
Both authors gratefully acknowledge the support of the PRODYN program of the European Science Foundation. HB was partially
supported by a fellowship of The Royal Netherlands Academy of Arts and Sciences (KNAW). SvS was partially supported by GR/M82714/01. 相似文献
2.
Goran Peskir 《Probability Theory and Related Fields》2002,124(1):100-111
Let (B
t
)
t
≥ 0) be a standard Brownian motion started at zero, let g : ℝ_+ →ℝ be an upper function for B satisfying g(0)=0, and let
be the first-passage time of B over g. Assume that g is C
1 on <0,∞>, increasing (locally at zero), and concave (locally at zero). Then the following identities hold for the density
function f of τ:
in the sense that if the second and third limit exist so does the first one and the equalities are valid (here is the standard normal density). These limits can take any value in [0,∞]. The method of proof relies upon the strong Markov
property of B and makes use of real analysis.
Received: 30 August 2001 / Revised version: 25 February 2002 / Published online: 22 August 2002 相似文献
3.
Travelling front solution for a class of competition-diffusion system with high-order singular point
In this paper, the existence of travelling front solution for a class of competition-diffusion system with high-order singular
point
is studied, where d
i,ai>0 (i=1,2) and w=(w
1(x,t),w
2(x,t)). Under the certain assumptions on f, it is showed that if a
i<1 for some i, then (1) has no travelling front solution, if a
i≥1 for i=1,2, then there is a c
0,c*>0, where c* is called the minimal wave speed of (I), such that if c≥c
0 or c=c*, then (I) has a travelling front solution, if c<c*, then (I) has no travelling front solution by using the shooting method in combination with a compactness argument.
Project supported by both the National (49772161) and Henan Province (984050300) Natural Science Foundations of China. 相似文献
| (I) |
4.
For given , c < 0, we are concerned with the solution f
b
of the differential equation f ′′′ + ff ′′ + g(f ′) = 0 satisfying the initial conditions f(0) = a, f ′ (0) = b, f ′′ (0) = c, where g is some nonnegative subquadratic locally Lipschitz function. It is proven that there exists b
* > 0 such that f
b
exists on [0, + ∞) and is such that as t → + ∞, if and only if b ≥ b
*. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising
in fluid mechanics, and especially in boundary layer theory.
相似文献
5.
Hui Yin Shuyue Chen Jing Jin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(6):969-1001
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers
equations
with prescribed initial data
Here v( > 0), β are constants, u
± are two given constants satisfying u
+ ≠ u
− and the nonlinear function f(u) ∈C
2(R) is assumed to be either convex or concave. An algebraic time decay rate to traveling waves of the solutions of the Cauchy
problem of generalized Benjamin-Bona-Mahony-Burgers equation is obtained by employing the weighted energy method developed
by Kawashima and Matsumura in [6] to discuss the asymptotic behavior of traveling wave solutions to the Burgers equation.
revised: May 23 and August 8, 2007 相似文献
6.
Stephen D. Fisher 《Israel Journal of Mathematics》1977,28(1-2):129-140
Letg be a positive continuous function onR which tends to zero at −∞ and which is not integrable overR. The boundary-value problem −u″+g(u)=f, u′(±∞)=0, is considered forf∈L
1(R). We show that this problem can have a solution if and only ifg is integrable at −∞ and if this is so then the problem is solvable precisely when ∫
−∞
∞
. Some extensions of this result are also given.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and by the National Science Foundation, Grant MPS
75-05501. 相似文献
7.
The existence of at least one positive solution and the existence of multiple positive solutions are established for the singular
second-order boundary value problem
using the fixed point index, where f may be singular at x=0 and px′=0.
The project is supported by the fund of National Natural Science (10571111) and the fund of Natural Science of Shandong Province. 相似文献
8.
In this paper, we will establish some new properties of traveling waves for integrodifference equations with the nonmonotone
growth functions. More precisely, for c ≥ c
*, we show that either limx?+￥ f(x)=u*{\lim\limits_{\xi\rightarrow+\infty} \phi(\xi)=u*} or 0 < liminfx? + ￥ f(x) < u* < limsupx?+￥f(x) ￡ b,{0 < \liminf\limits_{\xi \rightarrow + \infty} \phi(\xi) < u* < \limsup \limits_{\xi\rightarrow+\infty}\phi(\xi)\leq b,} that is, the wave converges to the positive equilibrium or oscillates about it at +∞. Sufficient conditions can assure that
both results will arise. We can also obtain that any traveling wave with wave speed c > c* possesses exponential decay at −∞. These results can be well applied to three types of growth functions arising from population
biology. By choosing suitable parameter numbers, we can obtain the existence of oscillating waves. Our analytic results are
consistent with some numerical simulations in Kot (J Math Biol 30:413–436, 1992), Li et al. (J Math Biol 58:323–338, 2009) and complement some known ones. 相似文献
9.
In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation
（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,
subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution. 相似文献
（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,
subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution. 相似文献
10.
Michael Bildhauer 《manuscripta mathematica》2003,110(3):325-342
Suppose that f: ℝ
nN
→ℝ is a strictly convex energy density of linear growth, f(Z)=g(|Z|2) if N>1. If f satisfies an ellipticity condition of the form
then, following [Bi3], there exists a unique (up to a constant) solution of the variational problem
provided that the given boundary data u
0
W
1
1
(ω;ℝ
N
) are additionally assumed to be of class L
∞(ω;ℝ
N
). Moreover, if μ<3, then the boundedness of u
0 yields local C
1,α-regularity (and uniqueness up to a constant) of generalized minimizers of the problem
In our paper we show that the restriction u
0L
∞(ω;ℝ
N
) is superfluous in the two dimensional case n=2, hence we may prescribe boundary values from the energy class W
1
1
(ω;ℝ
N
) and still obtain the above results.
Received: 12 February 2002 / Revised version: 7 October 2002 Published online: 14 February 2003
Mathematics Subject Classification (2000): 49N60, 49N15, 49M29, 35J 相似文献
11.
ＳＯＭＥＲＥＳＵＬＴＳＯＮＤＯＭＩＮＡＴＩＯＮＮＵＭＢＥＲＯＦＰＲＯＤＵＣＴＳＯＦＧＲＡＰＨＳＳＨＡＮＥＲＦＡＮＧＳＵＮＬＩＡＮＧＡＮＤＫＡＮＧＬＩＹＩＮＧＡｂｓｔｒａｃｔ．ＬｅｔＧ＝（Ｖ,Ｅ）ｂｅａｓｉｍｐｌｅｇｒａｐｈ．ＡｓｕｂｓｅｔＤｏｆＶｉｓ... 相似文献
12.
Zhu Ning 《高校应用数学学报(英文版)》1998,13(3):241-250
ＡＮＯＴＥＯＮＴＨＥＢＥＨＡＶＩＯＲＯＦＢＬＯＷ┐ＵＰＳＯＬＵＴＩＯＮＳＦＯＲＯＮＥ┐ＰＨＡＳＥＳＴＥＦＡＮＰＲＯＢＬＥＭＳＺＨＵＮＩＮＧＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｆｏｌｏｗｉｎｇｏｎｅ－ｐｈａｓｅＳｔｅｆａｎｐｒｏｂｌｅｍｉｓ... 相似文献
13.
Summary. We address the following problem from the intersection of dynamical systems and stochastic analysis: Two SDE dx
t
= ∑
j
=0
m
f
j
(x
t
)∘dW
t
j
and dx
t
=∑
j
=0
m
g
j
(x
t
)∘dW
t
j
in ℝ
d
with smooth coefficients satisfying f
j
(0)=g
j
(0)=0 are said to be smoothly equivalent if there is a smooth random diffeomorphism (coordinate transformation) h(ω) with h(ω,0)=0 and Dh(ω,0)=id which conjugates the corresponding local flows,
where θ
t
ω(s)=ω(t+s)−ω(t) is the (ergodic) shift on the canonical Wiener space. The normal form problem for SDE consists in finding the “simplest
possible” member in the equivalence class of a given SDE, in particular in giving conditions under which it can be linearized
(g
j
(x)=Df
j
(0)x).
We develop a mathematically rigorous normal form theory for SDE which justifies the engineering and physics literature on
that problem. It is based on the multiplicative ergodic theorem and uses a uniform (with respect to a spatial parameter) Stratonovich
calculus which allows the handling of non-adapted initial values and coefficients in the stochastic version of the cohomological
equation. Our main result (Theorem 3.2) is that an SDE is (formally) equivalent to its linearization if the latter is nonresonant.
As a by-product, we prove a general theorem on the existence of a stationary solution of an anticipative affine SDE.
The study of the Duffing-van der Pol oscillator with small noise concludes the paper.
Received: 19 August 1997 / In revised form: 15 December 1997 相似文献
14.
Let p be an odd prime, and f(x), g(x) ∈ [x]. Define
where is the inverse of x modulo p with ∈ {1, ..., p − 1}, and R
p
(x) denotes the unique r ∈ {0, 1, ..., p − 1} with x ≡ r(mod p). This paper shows that the sequences {e′
n
} is a “good” pseudorandom binary sequences, and give a generalization on a problem of D.H. Lehmer.
Supported by the National Natural Science Foundation of China under Grant No. 60472068 and No. 10671155; Natural Science Foundation
of Shaanxi province of China under Grant No. 2006A04; and the Natural Science Foundation of the Education Department of Shaanxi
Province of China under Grant No. 06JK168. 相似文献
15.
The existence of positive radial solutions of the equation -din( |Du|p-2Du)=f(u) is studied in annular domains in Rn,n≥2. It is proved that if f(0)≥0, f is somewherenegative in (0,∞), limu→0^ f‘ (u)=0 and limu→∞ (f(u)/u^p-1)=∞, then there is alarge positive radial solution on all annuli. If f(0)≤0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide. 相似文献
16.
Liguang Liu 《Frontiers of Mathematics in China》2007,2(4):599-611
Let ℐ(ℝn) be the Schwartz class on ℝn and ℐ∞(ℝn) be the collection of functions ϕ ∊ ℐ(ℝn) with additional property that
for all multiindices γ. Let (ℐ(ℝn))′ and (ℐ∞(ℝn))′ be their dual spaces, respectively. In this paper, it is proved that atomic Hardy spaces defined via (ℐ(ℝn))′ and (ℐ∞(ℝn))′ coincide with each other in some sense. As an application, we show that under the condition that the Littlewood-Paley
function of f belongs to L
p(ℝn) for some p ∊ (0,1], the condition f ∊ (ℐ∞(ℝn))′ is equivalent to that f ∊ (ℐ(ℝn))′ and f vanishes weakly at infinity. We further discuss some new classes of distributions defined via ℐ(ℝn) and ℐ∞(ℝn), also including their corresponding Hardy spaces.
相似文献
17.
Carl Mueller 《Probability Theory and Related Fields》1998,110(1):51-68
Summary. Let ? be the circle [0,J] with the ends identified. We prove long-time existence for the following equation.
Here, =(t,x) is 2-parameter white noise, and we assume that u
0(x) is a continuous function on ?. We show that if g(u) grows no faster than C
0(1+|u|)γ for some γ<3/2, C
0>0, then this equation has a unique solution u(t,x) valid for all times t>0.
Received: 27 November 1996 / In revised form: 28 July 1997 相似文献
18.
S. Treil 《Journal d'Analyse Mathématique》2002,87(1):481-495
The main result of the paper is that there exist functionsf
1,f
2,f inH
∞
satisfying the “corona condition”
such thatf
2 does not belong to the idealI generated byf
1,f
2, i.e.,f
2 cannot be represented as f2 ≡ f1g1 + f2g2, g1, g2 ∃ H∞. This gives a negative answer to an old question of T. Wolff [10].
It had been previously known under the same assumptions thatf
p
belongs to the ideal ifp > 2 but a counterexample can be constructed for p < 2; thus our casep = 2 is the critical one.
To get the main result, we improve lower estimates for the solution of the Corona Problem. Specifically, we prove that given
δ > 0, there exist finite Blaschke products f1, f2 satisfying the corona condition
such that for any g1,g2 ∃ H∞ satisfying f1g1 + f2g2 ≡ 1 (solution of the Corona Problem), the estimate |g1| ≥Cδ-2log(-log δ) holds. The estimate |g1|∞ ≥Cδ-2 was obtained earlier by V. Tolokonnikov.
Partially supported by NSF grant DMS-9970395. 相似文献
19.
Zaihong Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(4):592-608
In this paper, we study the existence of periodic solutions of Rayleigh equation
where f, g are continuous functions and p is a continuous and 2π-periodic function. We prove that the given equation has at least one 2π-periodic solution provided that f(x) is sublinear and the time map of equation x′′ + g(x) = 0 satisfies some nonresonant conditions. We also prove that this equation has at least one 2π-periodic solution provided that g(x) satisfies
and f(x) satisfies sgn(x)(f(x) − p(t)) ≥ c, for t ∈R, |x| ≥ d with c, d being positive constants.Received: July 1, 2002; revised: February 19, 2003Research supported by the National Natural Science Foundation of China, No.10001025 and No.10471099, Natural Science Foundation of Beijing, No. 1022003 and by a postdoctoral Grant of University of Torino, Italy. 相似文献
20.
Rostom Getsadze 《Journal d'Analyse Mathématique》2007,102(1):209-223
Let {ϕn(x), n = 1, 2,...} be an arbitrary complete orthonormal system on the interval I:= [0, 1]which consists of a.e. bounded functions. Suppose that E
0 ⊂ I
2 is any Lebesgue measurable set such that μ2
E
0 > 0, and φ, φ(0) = 0, is an increasing continuous function on [0, ∞) with φ(u) = o(u ln u) as u → ∞. Then there exist a function f ∈ L1(I
2) and a set E
0
′
, ⊂ E
0, μ2
E
0
′
> 0, such that
and the sequence of double Cesàro means of Fourier series of f with respect to the system {ϕn(x)ϕm(y): n,m = 1, 2,...} is unbounded in the sense of Pringsheim (by rectangles) on E
0
′
. This statement gives critical integrability conditions for the Cesàro summability a.e. of Fourier series in the class of
all complete orthonormal systems of the type {ϕ n(x)ϕm(y): n,m = 1, 2,...}. 相似文献