共查询到20条相似文献,搜索用时 15 毫秒
1.
With the notation
, we prove the following result. Theorem 1. Assume that p is a trigonometric polynomial of degree at most n with real coefficients that satisfies||p||L2(K)An1/2 and ||p′||L2(K)Bn3/2. ThenwithWe also prove that and for every
, where
denotes the collection of all trigonometric polynomials of the form 相似文献
2.
We consider a system of heat equations ut= Δu and vt= Δv in Ω×(0, T) completely coupled by nonlinear boundary conditions We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with for p, q>0, 0≤ α<1 and 0≤ β< p. 相似文献
3.
In this paper, we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m-point boundary-value problem for the one-dimensional p-Laplacian (φp(u′))′+f(t,u)=0, t(0,1), 相似文献
4.
Let B denote the unit ball of . For 0< p<∞, the holomorphic function spaces Qp and Qp,0 on the unit ball of are defined as and In this paper, we give some derivative-free, mixture and oscillation characterizations for Qp and Qp,0 spaces in the unit ball of . 相似文献
5.
In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ ∞∑j=-∞ψn-jεj, where {ε, εn; -∞< n < ∞}is a sequence of independent, identically distributed random variables with zero mean, μ>0 is a constant and the coefficients {ψi;-∞< i <∞} satisfy 0 <∞∑j=-∞|jψj| <∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ ∞∑j=-∞εjβnj) > x}is discussed. Then the result is applied to ultimate ruin probability. 相似文献
6.
We prove the Marcinkiewicz–Zygmund Strong Law of Large Numbers for U-statistics of strictly stationary, absolutely regular observations ( ξi) i≥1. Under suitable moment conditions and conditions on the mixing rate, we show that for some γ≥0, in the non-degenerate case, and in the degenerate case. 相似文献
7.
Let
be a probability space and let Pn be the empirical measure based on i.i.d. sample ( X1,…, Xn) from P. Let
be a class of measurable real valued functions on
For
define Ff( t):= P{ ft} and Fn,f( t):= Pn{ ft}. Given γ(0,1], define n,γ(δ):=1/( n1−γ/2δ γ). We show that if the L2( Pn)-entropy of the class
grows as −α for some α(0,2), then, for all
and all δ(0,Δ n), Δ n=O( n1/2), and where
and c(σ)↓1 as σ↓0 (the above inequalities hold for any fixed σ(0,1] with a high probability). Also, define Then for all
uniformly in
and with probability 1 (for
the above ratio is bounded away from 0 and from ∞). The results are motivated by recent developments in machine learning, where they are used to bound the generalization error of learning algorithms. We also prove some more general results of similar nature, show the sharpness of the conditions and discuss the applications in learning theory. 相似文献
8.
In this article, the authors consider equation ut = div(ψ(Гu)A(|Du|2)Du) -(u- I), where ψ is strictly positive and Г is a known vector-valued mapping, A: R → R is decreasing and A(s) ~ 1/√a as s → ∞. This kind of equation arises naturally from image denoising. For an initial datum I ∈ BVloc ∩ L∞, the existence of BV solutions to the initial value problem of the equation is obtained. 相似文献
9.
Let TR be a time-scale, with a=inf T, b=sup T. We consider the nonlinear boundary value problem | where λR+:=[0,∞), and satisfies the conditions We prove a strong maximum principle for the linear operator defined by the left-hand side of (1), and use this to show that for every solution (λ,u) of (1)–(2), u is positive on T a,b . In addition, we show that there exists λmax>0 (possibly λmax=∞), such that, if 0λ<λmax then (1)–(2) has a unique solution u(λ), while if λλmax then (1)–(2) has no solution. The value of λmax is characterised as the principal eigenvalue of an associated weighted eigenvalue problem (in this regard, we prove a general existence result for such eigenvalues for problems with general, nonnegative weights). 相似文献
10.
This article consider, for the following heat equation ut/|x|s-△pu=uq,(x,t)∈Ω×(0,T), u(x,t)=0,(x,t)∈(?)Ω×(0,T), u(x,0)=u0(x),u0(x)≥0,u0(x)(?)0 the existence of global solution under some conditions and give two sufficient conditions for the blow up of local solution in finite time, whereΩis a smooth bounded domain in RN(N>p),0∈Ω,△pu=div(|▽u|p-2▽u),0≤s≤2,p≥2,p-1相似文献
11.
We study generalized equations of the following form:
where
f is Fréchet differentiable in a neighborhood of a solution
x* of (*) and
g is Fréchet differentiable at
x* and where
F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (
xk) satisfying
which is super-linearly convergent to a solution of (*). We also present other versions of this iterative procedure that have superlinear and quadratic convergence, respectively.
相似文献
12.
This article discusses the perturbation of a non-symmetric Dirichlet form,(ε, D(ε)), by a signed smooth measure μ, whereμ=μ1 -μ2 with μ1 and μ2 being smooth measures. It gives a sufficient condition for the perturbed form (εμ, D(εμ)) (for some αo ≥ 0) to be a coercive closed form.
相似文献
13.
Let
be an orthonormal Jacobi polynomial of degree
k. We will establish the following inequality:
where
δ-1<
δ1 are appropriate approximations to the extreme zeros of
. As a corollary we confirm, even in a stronger form, T. Erdélyi, A.P. Magnus and P. Nevai conjecture [T. Erdélyi, A.P. Magnus, P. Nevai, Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994) 602–614] by proving that
in the region
.
相似文献
14.
In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations
in
Ω×(0,
T) with initial and Dirichlet boundary conditions, where
Ω is a bounded domain in
. Under suitable assumptions on the functions
gi(),
, the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property.
相似文献
15.
Unlike the non-singular case
s=0, or the case when 0 belongs to the interior of a domain Ω in
(
n3), we show that the value and the attainability of the best Hardy–Sobolev constant on a smooth domain Ω,
when 0<
s<2,
, and when 0 is on the boundary ∂Ω are closely related to the properties of the curvature of ∂Ω at 0. These conditions on the curvature are also relevant to the study of elliptic partial differential equations with singular potentials of the form:
where
f is a lower order perturbative term at infinity and
f(
x,0)=0. We show that the positivity of the sectional curvature at 0 is relevant when dealing with Dirichlet boundary conditions, while the Neumann problems seem to require the positivity of the mean curvature at 0.
相似文献
16.
Let, for example,
where
α>0,
k1, and exp
k=exp(exp(…exp())) denotes the
kth iterated exponential. Let {
An} denote the recurrence coefficients in the recurrence relation
xpn(x)=Anpn+1(x)+An-1pn-1(x)
for the orthonormal polynomials {
pn} associated with
W2. We prove that as
n→∞,
where log
k=log(log(…log())) denotes the
kth iterated logarithm. This illustrates the relationship between the rate of convergence to
of the recurrence coefficients, and the rate of decay of the exponential weight at ±1. More general non-even exponential weights on a non-symmetric interval (
a,
b) are also considered.
相似文献
17.
We present a new approach to the variational relaxation of functionals
of the type:
where
is a continuous function with growth conditions of order
p≥1 but not necessarily convex. We essentially study the case when μ is the
k-dimensional Hausdorff measure restricted to a suitable piece of a
k-dimensional smooth submanifold of
.
相似文献
18.
Let
ζ be the Riemann zeta function and
δ(
x)=1/(2
x-1). For all
x>0 we have
(1-δ(x))ζ(x)+αδ(x)<ζ(x+1)<(1-δ(x))ζ(x)+βδ(x),
with the best possible constant factors
This improves a recently published result of Cerone et al., J. Inequalities Pure Appl. Math. 5(2) (43) (2004), who showed that the double-inequality holds with and .
相似文献
19.
This paper deals with the existence of positive solutions for the one-dimensional
p-Laplacian
subject to the boundary value conditions:
where
p(
s)=|
s|
p−2s,
p>1. We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term
f is involved with the first-order derivative explicitly and
f may change sign.
相似文献
20.
For bounded Lipschitz domains
D in it is known that if 1<
p<∞, then for all
β[0,
β0), where
β0=
p−1>0, there is a constant
c<∞ with
for all . We show that if
D is merely assumed to be a bounded domain in that satisfies a Whitney cube-counting condition with exponent
λ and has plump complement, then the same inequality holds with
β0 now taken to be . Further, we extend the known results (see [H. Brezis, M. Marcus, Hardy's inequalities revisited, Dedicated to Ennio De Giorgi, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997–1998) 217–237; M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, A geometrical version of Hardy's inequality, J. Funct. Anal. 189 (2002) 537–548; J. Tidblom, A geometrical version of Hardy's inequality for
W1,p(
Ω), Proc. Amer. Math. Soc. 132 (2004) 2265–2271]) concerning the improved Hardy inequality
c=
c(
n,
p), by showing that the class of domains for which the inequality holds is larger than that of all bounded convex domains.
相似文献