共查询到20条相似文献,搜索用时 0 毫秒
1.
Alan V. Lair 《Applicable analysis》2013,92(5):431-437
We show that the equation Δu = p(x)f(u) has a positive solution on R N , N ≥ 3, satisfying <artwork name="GAPA31011ei1"> <artwork name="GAPA31011ei2"> if and only if <artwork name="GAPA31011ei3"> when ψ(r) = min{p(x): |x| = r}. The nondecreasing continuous function f satisfies f(0) = 0, f (s) > 0 for s > 0, and sup s ≥ 1 f(s)/s<∞, and the nonnegative continuous function p is required to be asymptotically radial. This extends previous results which required the function p to be constant or radial. 相似文献
2.
《复变函数与椭圆型方程》2012,57(7):555-568
A generalization of the Cauchy-Riemann condition in complex analysis is described for complex numbers, quaternions and complex quaternions. The generalization called here generalized Cauchy-Riemann-Fueter analycity encompasses not just the left and right-handed versions of quaternion analysis but also generates other variants for complex quaternions. These multiple variants are shown to satisfy an analogue of Cauchy's Theorem and to have similarities with the generalized Cauchy-Riemann conditions that define monogenic functions on R n + 1; they are also similar to Fueter-type operators and the Moisil-Theodoresco operator. The multiple variants are shown to have an interpretation that unifies analycity into a single definition. Thus left and right-handedness in quaternions are shown to be two sides of the same concept, and likewise for complex quaternions. This is then shown to have possible physical interpretation for example in understanding the nature of chirality and the 'arrow of time'. 相似文献
3.
By means of continuation theorem of coincidence degree theory, existence, nonexistence and unique existence criteria are established for the periodic solution of a kind of second order neutral functional differential equation. 相似文献
4.
ho Lijiang 《东北数学》1995,(4)
ExistenceTheoremofGlobalSolutionsforMonge-AmpereEquationhoLijiang(鹿立江)(TianjinUniversityofFinanceandEconomics,Tianjin,300222)... 相似文献
5.
Masaru Ikehata 《Applicable analysis》2013,92(9):857-873
We consider the problem of extracting information about an unknown inclusion embedded in a background layered material that has different constant conductivities across finitely many parallel planes, from the Dirichlet-to-Neumann map. For this purpose we construct the exponentially growing solutions of the governing equation for the background material. The leading coefficient of the equation has discontinuity across finitely many planes that are parallel to each other. Using the property of those solutions, we give an extraction formula of the support function of the inclusion from the Dirichlet-to-Neumann map. 相似文献
6.
Paolo Cianci 《Applicable analysis》2013,92(5):457-472
In this article, under some Hypotheses on weights and on coefficients, using a modification of Moser's method, we establish the boundedness of solutions of Dirichlet Problem for a class of nonlinear elliptic equations. 相似文献
7.
《Applicable analysis》2013,92(5):401-409
In this article, we obtain some results on the linearized oscillation of the odd-order neutral difference equation <artwork name="GAPA31013eu1"> where Δ is the forward difference operator, m is odd, {pn },{qn } are sequences of nonnegative real numbers, k, l are nonnegative integers, g(x),h(x)∈ C(R,R) with xg(x) > 0 for x ≠0. 相似文献
8.
邢家省 《数学物理学报(A辑)》2004,4(5):618-625
考虑半导体方程稳态模型的混合边值问题,应用Schauder不动点定理证明了逼近解的存在性,通过一系列先验估计的获得,利用紧致性原理证明了稳态解的存在性. 相似文献
9.
It is well-known that a semilinear parabolic equation has no unique solution in the classical sense. We study such equations
from the viewpoint of generalized functions. By using approximations for generalized functions, we obtain results on existence
and uniqueness of generalized solutions. Furthermore, we establish the relationship between generalized solutions and classical
solutions.
Current address: Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan 相似文献
10.
This article presents our computational results for imaging a seamount in a waveguide. We assume that there is no knowledge of what kind of boundary condition on the unknown seamount. The incident waves are sent from point sources along a straight line and the corresponding scattered fields are measured from a line above the unknown seamount. Analysis and numerical results are presented. 相似文献
11.
Concerning the obstacle-problem-like equation
, where + > 0 and – > 0, we give a complete characterization of all global two-phase solutions with quadratic growth both at 0 and infinity. 相似文献
12.
We show that a locally symmetric contact metric space is either Sasakian and of constant curvature 1 or locally isometric
to the unit tangent sphere bundle (with its standard contact metric structure) of a Euclidean space.
The second author is corresponding author 相似文献
13.
Let M
n
be an immersed umbilic-free hypersurface in the (n + 1)-dimensional unit sphere
, then M
n
is associated with a so-called M?bius metric g, a M?bius second fundamental form B and a M?bius form Φ which are invariants of M
n
under the M?bius transformation group of
. A classical theorem of M?bius geometry states that M
n
(n ≥ 3) is in fact characterized by g and B up to M?bius equivalence. A M?bius isoparametric hypersurface is defined by satisfying two conditions: (1) Φ ≡ 0; (2) All
the eigenvalues of B with respect to g are constants. Note that Euclidean isoparametric hypersurfaces are automatically M?bius isoparametrics, whereas the latter
are Dupin hypersurfaces.
In this paper, we determine all M?bius isoparametric hypersurfaces in
by proving the following classification theorem: If
is a M?bius isoparametric hypersurface, then x is M?bius equivalent to either (i) a hypersurface having parallel M?bius second fundamental form in
; or (ii) the pre-image of the stereographic projection of the cone in
over the Cartan isoparametric hypersurface in
with three distinct principal curvatures; or (iii) the Euclidean isoparametric hypersurface with four principal curvatures
in
. The classification of hypersurfaces in
with parallel M?bius second fundamental form has been accomplished in our previous paper [7]. The present result is a counterpart
of the classification for Dupin hypersurfaces in
up to Lie equivalence obtained by R. Niebergall, T. Cecil and G. R. Jensen.
Partially supported by DAAD; TU Berlin; Jiechu grant of Henan, China and SRF for ROCS, SEM.
Partially supported by the Zhongdian grant No. 10531090 of NSFC.
Partially supported by RFDP, 973 Project and Jiechu grant of NSFC. 相似文献
14.
George Costakis 《Monatshefte für Mathematik》2005,145(1):11-17
In this work we deal with universal Taylor series in the open unit disk, in the sense of Nestoridis; see [12]. Such series are not (C,k) summable at every boundary point for every k; see [7], [11]. In the opposite direction, using approximation theorems of Arakeljan and Nersesjan we prove that universal Taylor series can be Abel summable at some points of the unit circle; these points can form any closed nowhere dense subset of the unit circle. 相似文献
15.
一类微分差分方程的周期解 总被引:1,自引:0,他引:1
本文研究微分差分方程x'(t)=-f(x(t),x(t-τ1))-f(x(t),x(t-τ2))-...-f(x(t),x(t-τn))非平凡周期解的存在性问题,得到了一些判别准则,推广和改进了文[1-4]的工作。 相似文献
16.
Yuan Hongjun 《东北数学》1994,(4)
Solutions to the Equation of Non-Newtonian Polytropic Filtration Under Optimal Condition On Initial ValuesYuanHongjun(袁洪君)(De... 相似文献
17.
Marilyn Breen 《Monatshefte für Mathematik》2006,148(2):91-100
For n ≥ 1, define p (n) to be the smallest natural number r for which the following is true: For
any finite family of simply connected orthogonal polygons in the plane and points x and y in
, if every r (not necessarily distinct) members of
contain a common staircase n-path from x to y, then
contains such a path. We show that p(1) = 1 and p(n) = 2 (n − 1) for n ≥ 2. The numbers p(n) yield an improved Helly theorem for intersections of sets starshaped via staircase n-paths.
Moreover, we establish the following dual result for unions of these sets: Let
be any finite family of orthogonal polygons in the plane, with
simply connected. If every three (not necessarily distinct) members of
have a union which is starshaped via staircase n-paths, then T is starshaped via staircase (n + 1)-paths. The number n + 1 in the theorem is best for every n ≥ 2. 相似文献
18.
Plateau's problem (PP) is studied for surfaces of prescribed mean curvature spanned by a given contour in a 3-d Riemannian
manifold. We consider the local situation where a neighborhood of a given point on the manifold is described by a single normal
chart. Under certain conditions on and the contour, existence of a small -surface to (PP) is guaranteed by [HK]. The purpose of this paper is the investigation of large -surfaces. Our result states: For sufficiently large (constant) mean curvature and a sufficiently small contour depending
on the local geometry of the manifold, (PP) has at least two solutions, a small one and a large one. The proof is based on
mountain pass arguments and uses – in contrast to results in the 3-d Euclidean space and in order to derive conformality directly
– also a deformation constructed by variations of the independent variable.
Received November 8, 1995 / Accepted April 29, 1996 相似文献
19.
An element σ of An, the Alternating group of degree n, is extendible in Sn, the Symmetric group of degree n, if there exists a subgroup H of Sn but not An whose intersection with An is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of An to be extendible in Sn is given here. 相似文献
20.
Several existence theorems on multiple positive radial solutions of the elliptic boundary value problem in an exterior domain
are obtained by using the fixed point index theory. Our conclusions are essential improvements of the results in [7], [10]
and [13]. 相似文献