共查询到20条相似文献,搜索用时 29 毫秒
1.
Aleksandar Ivić 《Central European Journal of Mathematics》2005,3(2):203-214
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If E
*(t)=E(t)-2πΔ*(t/2π) with
, then we obtain
and
It is also shown how bounds for moments of | E
*(t)| lead to bounds for moments of
. 相似文献
2.
Luisa Fattorusso 《Czechoslovak Mathematical Journal》2008,58(1):113-129
Let Ω be a bounded open subset of ℝ
n
, n > 2. In Ω we deduce the global differentiability result
for the solutions u ∈ H
1 (Ω, ℝ
n
) of the Dirichlet problem
with controlled growth and nonlinearity q = 2.
The result was obtained by first extending the interior differentiability result near the boundary and then proving the global
differentiability result making use of a covering procedure. 相似文献
3.
This paper deals with the existence of weak solutions in W
01(Ω) to a class of elliptic problems of the form
in a bounded domain Ω of ℝ
N
. Here a satisfies
for all ξ∈ℝ
N
, a.e. x∈Ω,
, h
1∈L
loc
1(Ω), h
1(x)≧1 for a.e. x in Ω; λ
1 is the first eigenvalue for −Δ
p
on Ω with zero Dirichlet boundary condition and g, h satisfy some suitable conditions.
相似文献
4.
GuoEnHU 《数学学报(英文版)》2003,19(2):397-404
The L^2(R^n) boundedness for the multilinear singular integral operators defined by TAf(x)=∫R^nΩ(x-y)/|x-y|^n 1(A(x)-A(y)-△↓A(y)(x-y))f(y)dy is considered,where Ω is homogeneous of degree zero,integrable on the unit sphere and has vanishing moment of order one,A has derivatives of order one in BMO(R^n) boundedness for the multilinear operator TA is given. 相似文献
5.
Choonkil Park 《Acta Appl Math》2008,102(1):71-85
This paper is a survey on the Hyers–Ulam–Rassias stability of the following Cauchy–Jensen functional equation in C
*-algebras:
The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias’ stability theorem (Rassias in Proc. Am. Math.
Soc. 72:297–300, [1978]).
This work was supported by the research fund of Hanyang University (HY-2007-S). 相似文献
6.
Xianling Fan Shao-Gao Deng 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):255-271
We study the existence and multiplicity of positive solutions for the inhomogeneous Neumann boundary value problems involving
the p(x)-Laplacian of the form
where Ω is a bounded smooth domain in , and p(x) > 1 for with and φ ≢ 0 on ∂Ω. Using the sub-supersolution method and the variational method, under appropriate assumptions on f, we prove that, there exists λ* > 0 such that the problem has at least two positive solutions if λ = λ*, has at least one positive solution if λ = λ*, and has no positive solution if λ = λ*. To prove the result we establish a special strong comparison principle for the Neumann problems.
The research was supported by the National Natural Science Foundation of China 10371052,10671084). 相似文献
7.
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
8.
9.
Aleksandar Ivić 《Central European Journal of Mathematics》2004,2(4):494-508
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If
with
, then we obtain
. We also show how our method of proof yields the bound
, where T
1/5+ε≤G≪T, T<t
1<...<t
R
≤2T, t
r
+1−t
r
≥5G (r=1, ..., R−1). 相似文献
10.
MUCHUNLAI TANGXIANJIANG 《高校应用数学学报(英文版)》1998,13(1):31-38
In this paper L^p-L^q estimates for the solution u(x,t) to the following perturbed high-er order hyperbolic equation are considered, (ρπ--a△)(ρπ--b△)u V(x)u=O, x∈R^n,n≥6, ρ1eu(x,O) = O, ρ^3eu(x,O) = f(x), (j = O,1,2).We assume that the otential V(x) and the initial data f(x) are compactly supported, andV(x) is sufficiently small, then the solution u (x,t) of the above problem satisfies the same L^p-L^q estimates as that of the unperturbed problem. 相似文献
11.
In this paper we consider the Lane–Emden problem adapted for the p-Laplacian
where Ω is a bounded domain in , n ≥ 2, λ > 0 and p < q < p* (with if p < n, and p* = ∞ otherwise). After some recalls about the existence of ground state and least energy nodal solutions, we prove that,
when q → p, accumulation points of ground state solutions or of least energy nodal solutions are, up to a “good” scaling, respectively
first or second eigenfunctions of −Δ
p
.
Received: 29 April 2008 相似文献
12.
LiJunjie BianBaojun 《高校应用数学学报(英文版)》2000,15(3):273-280
The following regularity of weak solutions of a class of elliptic equations of the form are investigated. 相似文献
13.
Sandro Zagatti 《Calculus of Variations and Partial Differential Equations》2008,31(4):511-519
We consider a class of non convex scalar functionals of the form
under standard assumptions of regularity of the solutions of the associated relaxed problem and of local affinity of the bipolar
f
** of f on the set {f
** < f}. We provide an existence theorem, which extends known results to lagrangians depending explicitly on the three variables,
by the introduction of integro-extremal minimizers of the relaxed functional which solve the equation
or the opposite one, almost everywhere and in viscosity sense. 相似文献
14.
Concentration of mass on convex bodies 总被引:2,自引:0,他引:2
G. Paouris 《Geometric And Functional Analysis》2006,16(5):1021-1049
We establish sharp concentration of mass inequality for isotropic convex bodies: there exists an absolute constant c > 0 such that if K is an isotropic convex body in
, then
for every
, where LK denotes the isotropic constant.
Research supported by a Marie Curie Intra-European Fellowship (EIF), Contract MEIF-CT-2005-025017. Part of this work was done
while the author was a Postdoctoral Fellow at the University of Athens under the EPEAEK program “Pythagoras II”.
Received: January 2006; Revision: March 2006; Accepted: March 2006 相似文献
15.
CongWenLIU JiHuaiSHI 《数学学报(英文版)》2003,19(1):187-200
In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f(φ(0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting. 相似文献
16.
José Maria Gomes 《Archiv der Mathematik》2007,88(3):269-278
Let Ω be a bounded convex domain in
. We consider constrained minimization problems related to the Euler-Lagrange equation
over classes of functions
(Ω) with convex super level sets. We then search for sufficient conditions ensuring that the minimizer obtained is a classical
solution to the above equation.
Supported by ESF activity “Global and geometrical aspects of nonlinear P.D.E.’s.”
Received: 4 April 2006 相似文献
17.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
18.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
19.
Given a connected open set
and a function w ∈LN/p(Ω) if 1 < p < N and w ∈Lr (Ω) for some r ∈(1, ∞) if p ≧ N, with
we prove that the positive principal eigenvalue of the problem
is unique and simple. This improves previous works all of which assumed w in a smaller space than LN/p (Ω) to ensure that Harnack’s inequality holds. Our proof does not rely on Harnack’s inequality, which may fail in our case.
Received: 18 March 2005; revised: 7 April 2005 相似文献
20.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp(0〈p〈1)Spaces 总被引:1,自引:0,他引:1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献