共查询到20条相似文献,搜索用时 15 毫秒
1.
Franco Cardin Marco Favretti 《NoDEA : Nonlinear Differential Equations and Applications》1998,5(3):397-406
In this paper we define a notion of injectivity for a vector field over a Riemannian manifold and we give a sufficient condition
for it. The proof is an extension of a well known Theorem stating that a map from an open convex set of the euclidean space
into is a diffeomorphism onto its image provided that the bilinear operator associated to its differential is (positive or negative)
definite everywhere. In the second part of the paper, we show that these results have a natural extension to the tangent bundle,
with straightforward applications to second order differential equations.
Received May 3, 1997 - Revised version received October 21, 1997 相似文献
2.
In this paper we give a systematized treatment to some coincidence situations for multiple summing multilinear mappings which extend, generalize and simplify the methods and results obtained thus far. The application of our general results to the pertinent particular cases gives several new coincidences as well as easier proofs of some known results (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A variational theory for monotone vector fields 总被引:1,自引:0,他引:1
Nassif Ghoussoub 《Journal of Fixed Point Theory and Applications》2008,4(1):107-135
Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators,
but also as natural extensions of gradients of convex potentials. These vector fields are not always derived from potentials
in the classical sense, and as such they are not always amenable to the standard methods of the calculus of variations. We
describe here how the selfdual variational calculus, developed recently by the author, provides a variational approach to
PDEs and evolution equations driven by maximal monotone operators. To any such vector field T on a reflexive Banach space X, one can associate a convex selfdual Lagrangian L
T
on the phase space X × X
* that can be seen as a “potential” for T, in the sense that the problem of inverting T reduces to minimizing a convex energy functional derived from L
T
. This variational approach to maximal monotone operators allows their theory to be analyzed with the full range of methods—computational
or not—that are available for variational settings. Standard convex analysis (on phase space) can then be used to establish
many old and new results concerned with the identification, superposition, and resolution of such vector fields.
Dedicated to Felix Browder on his 80th birthday 相似文献
5.
Various concepts of invariant monotone vector fields on Riemannian manifolds are introduced. Some examples of invariant monotone vector fields are given. Several notions of invexities for functions on Riemannian manifolds are defined and their relations with invariant monotone vector fields are studied. 相似文献
6.
We consider strongly monotone continuous planar vector fields with a finite number of fixed points. The fixed points fall into three classes, attractors, repellers and saddles. Naturally, the relative positions of the fixed points must obey a set of restrictions imposed by monotonicity. The study of these restrictions is the main goal of the paper. With any given vector field, we associate a matrix describing the arrangement of the fixed points on the plane. We then use these matrices to formulate simple necessary and sufficient conditions which allow one to determine whether a finite set of attractors, repellers and saddles at given positions on the plane can be realized as the fixed point set of a strongly monotone vector field. 相似文献
7.
A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping 总被引:5,自引:5,他引:0
The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space. 相似文献
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A. R. Alimov 《Mathematical Notes》2012,91(1-2):290-292
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In this paper, we deal with invex equilibrium problems (IEPs for short). When the constraint set is compact convex, an existence result of solutions is obtained by Schauder's fixed point theorem. If the constraint set is closed invex, we introduce the concept of relaxed α–η pseudomonotone mappings and prove some existence results of solutions for the (IEPs), which extend and generalize several well‐known results in many respects. Moreover, we present that if the IEPs are applied to hemivariational inequalities problems, the conditions can be weakened. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
Yu. L. Ershov 《Siberian Advances in Mathematics》2011,21(4):259-261
Proposition 1 of this article points at a gap in the proof of Kuhlmann’s characterization of algebraically maximal valued
fields [2]. The author [1] showed how to fill this gap. His arguments involved tools of mathematical logic and infinite combinatorics.
Proposition 2 of this article provides us with a simple proof of the key fact of Kuhlmann’s characterization. 相似文献
12.
Márcia Federson 《Czechoslovak Mathematical Journal》2002,52(2):429-437
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil,
, where R is a compact interval of
, and f are functions with values on L(Z,W) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral,
, as well as to unbounded intervals R. 相似文献
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We study heat-bath Glauber dynamics for the ferromagnetic Ising model on a finite cycle (a graph where every vertex has degree two). We prove that the relaxation time 2 is an increasing function of any of the couplings J
xy
. We also prove some further inequalities, and obtain exact asymptotics for 2 at low temperatures.
Mathematics Subject Classification (2000):60K35, 82C20 相似文献
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In this paper we prove a unique continuation property for vector valued functions of one variable satisfying certain differential inequality. 相似文献
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We study the structure of the most common type of Riemannian submersions, namely those whose fibers are given by the orbits
of an isometric group action on a Riemannian manifold. Special emphasis is given to the case where the ambient space has nonnegative
curvature.
The first author was supported by research grant MTM2004-04794-MEC. Most of this work was done during a visit of the second
author to Madrid, financed in part by funds of the aforementioned grant. 相似文献
20.
A space X is said to satisfy condition (C) if for every Y?X with |Y|=ω1, any family of open subsets of Y with ||=ω1 has a countable network. It is easy to see that if X satisfies condition (C), then its Pixley-Roy hyperspace [X] is CCC. We show that under MAω1 condition (C) is also necessary for [X] to be CCC, but under CH it is not. 相似文献