共查询到20条相似文献,搜索用时 31 毫秒
1.
We study the existence of classical (non-collision) T-periodic
solutions of the Hamiltonian system
where
and
is a T-periodic function in t which has a
singularity at
like
Under suitable conditions on H, we prove that if
then (HS) possesses at least one
non-collision solution and if
then the generalized solution of (HS) obtained in [5] has at most
one time of collision in its period. 相似文献
2.
We study the application,
, where
is the
supremum of positive s such that the problem
admits a solution. Where B 1 is the unit ball in
We show that
is a decreasing function, with
where
is the unique solution of the
problem
.
We also give the explicit solutions of the problem
, when
and show that
. We show that the problem
doesnt admit a solution.
In the end, we give a numerical approximation of
, when
. 相似文献
3.
In this note we prove the uniqueness of U in a group G with
a spherical split-BN-pair of rank
,i.e., if G has such a BN-pair with
a nilpotent normal subgroup of B,
and
, then
and
is a normal subgroup of G. Here
is the corresponding group of Lie-type and
the subgroup of
generated by all root-subgroups corresponding to positive roots.
Received: 19 May 2003 相似文献
4.
In this paper we shall consider the critical elliptic
equation
where
and a(x)
is a real continuous, non
negative function, not identically zero. By using a local Pohozaev
identity, we show that problem (0.1) does not admit a
family of solutions
which blows-up and concentrates as
at some zero point x0 of a(x)
if the order of flatness of the function a(x) at x0 is
相似文献
5.
Let p be a prime,
a finite p-group,
any finite group with order divisible by p,
and
any action of
on
. We show that the cardinality of the set of all derivations
with respect to this action is a multiple of
p. This
generalises theorems of Frobenius and Hall.
Received: 16 June 2003 相似文献
6.
Let
be the Hecke algebra of the symmetric group
over a field K of characteristic
and
a primitive
-th root of one in K. We show that an
-module is projective if and only if its restrictions to any
-parabolic subalgebra of
is projective.
Moreover, we give a new construction of blocks of
-parabolic subalgebras, in terms of skew group algebras over local commutative
algebras.
Received: 30 June 2003 相似文献
7.
Let p be a prime, G
a finite group which has a normal p-subgroup
containing its own centralizer in G, and
R a commutative local ring with residue class
field of characteristic p. In this paper, it is
shown that if
is an augmented automorphism of
RG which fixes a Sylow
p-subgroup P
of G, there is
such that
for all
and
is an inner automorphism of
RG.
Received: 26 July 2000 相似文献
8.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献
9.
R. B. Kusner [R. Guy, Amer. Math. Monthly 90, 196-199 (1983)]
asked whether a set of vectors in
such that the
distance between any pair is 1, has cardinality at most
d + 1.
We show that this is true for p = 4
and any
, and false for all 1<p<2 with d sufficiently large, depending on p. More
generally we show that the maximum cardinality is at most
if p is an even integer, and at least
if 1<p<2, where
depends on p.
Received: 5 May 2003 相似文献
10.
Let p be a prime number.
Let G be a finite
p-group and
. Denote by
the complex conjugate of
. Assume that
. We show that the number of
distinct irreducible constituents of the product
is at least
.
Received: 17 March 2003 相似文献
11.
Zhaoli Liu Zhi-Qiang Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(4):609-629
We obtain the existence of infinitely many nodal solutions for the Schrödinger type equation on
with
Here,
The nonlinearity f is symmetric in the sense of being odd in u, and may involve a combination of concave and convex terms.Received: November 11, 2003; revised: December 12, 2004Supported by NSFC:10441003 相似文献
12.
We consider the problem
in a smooth boundary domain
, as well
as the corresponding evolution equation
. For the stationary equation
we show existence results, then we adapt the techniques of doubling of variables
to the case of the homogeneous Neumann boundary conditions and obtain the
appropriate L
1
-contraction principle and uniqueness. Subsequently, we are able to apply the
nonlinear semigroup theory and prove the L
1
-contraction principle for the associated evolution equation. 相似文献
13.
Marilyn Breen 《Aequationes Mathematicae》2004,67(3):263-275
Summary.
We establish the following Helly-type result for infinite families
of starshaped sets in
Define the function f on
{1, 2} by
f(1) = 4,
f(2) = 3.
Let
be a fixed positive number, and let
be a uniformly bounded family of compact sets
in the plane. For k = 1, 2, if every
f(k)
(not necessarily distinct) members of
intersect in a starshaped set whose
kernel contains a k-dimensional
neighborhood of radius
, then
is a starshaped set whose kernel is at least
k-dimensional.
The number f(k) is best in each case.
In addition, we present a few results concerning the dimension of
the kernel in an intersection of starshaped sets in
Some of these involve finite families of sets, while others
involve infinite families and make use of the Hausdorff metric. 相似文献
14.
In this paper, using the generalized Wronskian, we obtain a new sharp
bound for the generalized Masons theorem [1] for functions of several variables.
We also show that the Diophantine equation (The generalized Fermat-Catalan equation)
where
, such that k out of the
n-polynomials
are constant, and
under certain conditions for
has no non-constant solution.
Received: 20 March 2003 相似文献
15.
16.
The solutions of the equation
in
, where
are investigated,
Bessel potentials of higher order are defined, and recurrence relations
between these solutions and these Bessel potentials are obtained. It is
also proved that these solutions and the solutions of
, under certain conditions, are identical.
Received: 6 November 2002 相似文献
17.
Simona Dabuleanu 《Journal of Evolution Equations》2005,5(1):35-60
We study the weak solvability of viscous Hamilton-Jacobi equation:
\,0,\,x\,\in\,\Omega,$" align="middle" border="0">
with Neumann boundary condition and irregular initial data 0. The domain
is a bounded open set and p > 0. The last part deals with the case a convex set and the initial data 0 = in a open set D such that
and
相似文献
18.
Marilyn Breen 《Archiv der Mathematik》2005,84(3):282-288
Let k and d be fixed integers, 0kd, and let
be a collection of sets in
If every countable subfamily of
has a starshaped intersection, then
is (nonempty and) starshaped as well. Moreover, if every countable subfamily of
has as its intersection a starshaped set whose kernel is at least k-dimensional, then the kernel of
is at least k-dimensional, too. Finally, dual statements hold for unions of sets.Received: 3 April 2004 相似文献
19.
Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献