共查询到20条相似文献,搜索用时 0 毫秒
1.
We prove the existence of non-smooth solutions to fully non-linear elliptic equations.
Received: June 2006, Accepted: January 2007 相似文献
2.
M. A. Nudelman 《Integral Equations and Operator Theory》2007,58(2):273-299
Let
I
m
is the identity matrix of order m. Let W(λ) be an entire matrix valued function of order 2m, W(0) = I
2m
, the values of W(λ) are j
mm
-unitary at the imaginary axis and strictly j
mm
-expansive in the open right half-plane. The blocks of order m of the matrix W(λ) with appropriate signs are treated as coefficients of algebraic Riccati equation. It is proved that for any λ with positive
real part this equation has a unique contractive solution θ(λ). The matrix valued function θ(λ) can be represented in a form θ(λ) = θ
A
(iλ) where θ
A
(μ) is the characteristic function of some maximal dissipative operator A. This operator is in a natural way constructed starting from the Hamiltonian system of the form
with periodic coefficients. 相似文献
3.
We develop a theoretical framework for projection-iterative methods to solve operator equations of the form Au + Bu = f, where A is a Toeplitz operator in a Banach space , B is considered as a perturbation (of general form) of A, and f is a given element in this space. The methods are adopted for application to general situations, in particular, to the equations
in which A need not be a Fredholm operator. The idea to involve iteration procedures and the technique which we apply allow to obtain
conditions on perturbations for convergence and effective error estimates in terms of some weighted spaces (without any restrictions
on the norms for perturbations). Based on established evaluations we derive further information about decaying properties
of the solutions. The obtained results are illustrated by considering concrete classes of equations as, for instance, equations
corresponding to Jacobi type operators.
相似文献
4.
Elena I. Kaikina Leonardo Guardado-Zavala Hector F. Ruiz-Paredes Jesus A. Mendez Navarro 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):63-77
We study nonlinear nonlocal equations on a half-line in the critical case
where . The linear operator is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol , the number . The aim of this paper is to prove the global existence of solutions to the inital-boundary value problem (0.1) and to find
the main term of the large time asymptotic representation of solutions in the critical case.
相似文献
5.
Blow-up Solutions for Mixed Nonlinear Schrodinger Equations 总被引:1,自引:0,他引:1
ShaoBinTAN 《数学学报(英文版)》2004,20(1):115-124
This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation: Фt=iαФxx βФ^2Ф^-x γ|Ф|^2Фx ig(|Ф|^2)Ф Under certain conditions on the initial data and the function g(s),we study the existence and nonexistence of global solution for this equation.The blow-up solution and the blow-up time are also investigated. 相似文献
6.
Michael Kapovich 《Geometric And Functional Analysis》2009,18(6):2017-2054
We prove an inequality between the relative homological dimension of a Kleinian group and its critical exponent. As an application of this result we show that for a geometrically finite Kleinian group Γ, if
the topological dimension of the limit set of Γ equals its Hausdorff dimension, then the limit set is a round sphere.
Received: March 2007, Revision: October 2007, Accepted: October 2007 相似文献
7.
We consider a simple Allen-Cahn-Gurtin model with a logarithmic potential. We show that strong solutions exist locally in
time, but not globally in general. This is due to a lack of maximum principle.
相似文献
8.
Dong-Gun Park Jin-Mun Jeong Han-Geul Kim 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):235-253
In this paper we establish the wellposedness and regularity properties of solutions of Cauchy problems for semilinear hyperbolic
equations of second order with unbounded principal operators. An example illustrating how our results apply is given.
相似文献
9.
We consider the semilinear reaction diffusion equation
, in a bounded domain . We assume the standard “Allen-Cahn-type” nonlinearity, while V is either the inverse square potential or the borderline potential (thus including the classical Allen-Cahn-type equation as a special case when ). In the subcritical cases and where is the optimal constant of Hardy and Hardy-type inequalities), we present a new estimate on the dimension of the global attractor.
This estimate comes out by an improved lower bound for sums of eigenvalues of the Laplacian by A. D. Melas (Proc. Amer. Math.
Soc. 131 (2003), 631–636). The estimate is sharp, revealing the existence of (an explicitly given) threshold value for the ratio of
the volume to the moment of inertia of Ω on which the dimension of the attractor may considerably change. Consideration is
also given on the finite dimensionality of the global attractor in the critical case
Received: 7 May 2008 相似文献
10.
Generalizing earlier results, it is shown that if are “large” subsets of a finite field F
q
, then the equations a + b = cd, resp. ab + 1 = cd can be solved with . Other algebraic equations with solutions restricted to “large” subsets of F
q
are also studied. The proofs are based on character sum estimates proved in Part I of the paper.
Research partially supported by the Hungarian National Foundation for Scientific Research, Grants No. T 043623, T 043631 and
T 049693. 相似文献
11.
Nonlinear electroelastostatics: a variational framework 总被引:2,自引:0,他引:2
R. Bustamante A. Dorfmann R. W. Ogden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(1):154-177
Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and
two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential
and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables
are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and
some differences highlighted.
相似文献
12.
Marcus Carlsson 《Integral Equations and Operator Theory》2008,61(4):593-598
In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M
z
on a Hilbert space -valued analytic functions, where M
z
denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s
theorem.
In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works
for Banach space operators.
相似文献
13.
J. William Helton Daniel P. McAllaster Joshua A. Hernandez 《Integral Equations and Operator Theory》2008,61(1):77-102
The paper introduces a notion of the Laplace operator of a polynomial p in noncommutative variables x = (x
1,…, x
g
). The Laplacian Lap[p, h] of p is a polynomial in x and in a noncommuting variable h. When all variables commute we have Lap[p, h] = h
2Δ
x
p where Δ
x
p is the usual Laplacian. A symmetric polynomial in symmetric variables will be called harmonic if Lap[p, h] = 0 and subharmonic if the polynomial q(x, h) := Lap[p, h] takes positive semidefinite matrix values whenever matrices X
1,…, X
g
, H are substituted for the variables x
1,…, x
g
, h. In this paper we classify all homogeneous symmetric harmonic and subharmonic polynomials in two symmetric variables. We
find there are not many of them: for example, the span of all such subharmonics of any degree higher than 4 has dimension
2 (if odd degree) and 3 (if even degree). Hopefully, the approach here will suggest ways of defining and analyzing other partial
differential equations and inequalities.
Dedicated to Israel Gohberg on the occasion of his 80th birthday.
All authors were partially supported by J.W. Helton’s grants from the NSF and the Ford Motor Co. and J. A. Hernandez was supported
by a McNair Fellowship. 相似文献
14.
Eduardo Hernández Morales Hernán R. Henríquez Mark A. McKibben 《Integral Equations and Operator Theory》2008,62(2):191-217
We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations
with unbounded delay in a Banach space.
The work of the second author was supported by FONDECYT-CONICYT, Grants 1050314 and 7050034. 相似文献
15.
The validity of the axiomatization of the Harsanyi solution for NTU-games by Hart (1985) is shown to depend on the regularity conditions imposed on games. Following this observation, we propose two related axiomatic characterizations, one of the symmetric egalitarian solution (Kalai and Samet, 1985) and one of the consistent solution (Maschler and Owen, 1992). The three axiomatic results are studied, evaluated and compared in detail.Revised October 2004We thank an anonymous referee and an associate editor for their helpful comments. Geoffroy de Clippel also thanks Professors Sergiu Hart, Jean-François Mertens and Enrico Minelli. Horst Zank thanks the Dutch Science Foundation NWO and the British Council for support under the UK-Netherlands Partnership Programme in Science (PPS 706). The usual disclaimer applies. 相似文献
16.
J. L. García-Roig Emma Martín-Gutiérrez 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2000,70(1):85-92
We solve the functional equationf(x
3 +y
3) =f(x)3 +f(y)3 for maps of a finite field into itself. 相似文献
17.
18.
Egbert Harzheim 《Order》2008,25(2):79-83
We construct a subset of the set R of real numbers of cardinality |R| which has a similarity decomposition, and which has
an ordertype < that of R. Seymour Ginsburg had posed the question whether there exist sets with another ordertype than that
of R which also have a similarity decomposition.
相似文献
19.
We prove that a tournament with n vertices has more than arc-disjoint transitive triples, and more than arc-disjoint transitive quadruples, improving earlier bounds. In particular, 82 percent of the arcs of a tournament can be
packed with transitive triples and 45 percent of the arcs of a tournament can be packed with transitive quadruples. Our proof
is obtained by examining the fractional version of the problem and utilizing a connection between the integral and fractional
versions.
Received October 12, 2005 相似文献