共查询到20条相似文献，搜索用时 31 毫秒
1.
In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form
It is shown that this equilibrium is Ljapounov stable under small perturbations in
where
provided that the parameters a, b, , are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques.Received: February 5, 2003; revised: September 29, 2003Dedicated to Prof. H. Amann on the occasion of his 65. birthday 相似文献
2.
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk | z| < 1 satisfying the condition
|
$
\frac{{f(z)}}
{z} \ne 0and\left| {f'(z)\left( {\frac{z}
{{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.
$
\frac{{f(z)}}
{z} \ne 0and\left| {f'(z)\left( {\frac{z}
{{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.
相似文献
3.
We are interested in parabolic problems with L1 data of the type
with i, j=0, 1, ( i, j) (0, 0), 0 = 0 and 1 = 1. Here, is an open bounded subset of
with regular boundary and
is a Caratheodory function satisfying the classical Leray-Lions conditions and is a monotone graph in
with closed domain and such that
We study these evolution problems from the point of view of semi-group theory, then we identify the generalized solution of the associated Cauchy problem with the entropy solution of
in the usual sense introduced in [5]. 相似文献
4.
Let be the class of functions which are holomorphic and convex in direction in the unit disk , i.e. the domain is such that the intersection of and any straight line is a connected or empty set. In this note we determine the radius of the biggest disk with the property that each function maps this disk onto the convex domain in the direction . 相似文献
5.
An algorithm for constructing the operator O Mn({ kx}; x, y) with the properties |
n, \hfill \\ \frac{{\partial ^n O_{Mn} (\{ \varphi _{ks} \} ;x,y)}}{{\partial v_a^p }}|_{\Gamma _a } = \varphi _{ap} (x,y)|_{\Gamma _Q '} q = \overline {1, M} ; p = \overline {0, n,} \hfill \\ \end{gathered} $$
" align="middle" vspace="20%" border="0"> 相似文献
6.
For a circle write . A continuous function on extends holomorphically from (into the disc bounded by ) if and only if the function defined on has a bounded holomorphic extension into . In the paper we consider open connected families of circles , write , and assume that a continuous function on extends holomorphically from each . We show that this happens if and only if the function defined on has a bounded holomorphic extension into the domain for each open family compactly contained in . This allows us to use known facts from several complex variables. In particular, we use the edge of the wedge theorem to prove a theorem on real analyticity of such functions. 相似文献
7.
The existence of at least one solution of the following multi-point boundary value problem
|
$
\left\{ \begin{gathered}
[\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\
x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\
x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
[\varphi (x'(t))]' = f(t,x(t),x'(t)),t \in (0,1), \hfill \\
x(0) - \sum\limits_{i = 1}^m {\alpha _i x'(\xi _i ) = 0,} \hfill \\
x'(1) - \sum\limits_{i = 1}^m {\beta _i x(\xi _i ) = 0} \hfill \\
\end{gathered} \right.
相似文献
8.
We consider the first-order Cauchy problem
|
$
\begin{gathered}
\partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\
u|_{z = 0} = u_0 , \hfill \\
\end{gathered}
$
\begin{gathered}
\partial _z u + a(z,x,D_x )u = 0,0 < z \leqslant Z, \hfill \\
u|_{z = 0} = u_0 , \hfill \\
\end{gathered}
相似文献
9.
Suppose that X is a complex Banach space with the norm ‖·‖ and n is a positive integer with dim X ⩾ n ⩾ 2. In this paper, we consider the generalized Roper-Suffridge extension operator $
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
on the domain $
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
$
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
defined by
|
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = {*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = \begin{array}{*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
\end{array}
相似文献
10.
In this paper, we obtain asymptotic bounds, under appropriate conditions, of solutions of third order difference equations
of the form
|
$
\Delta (p_{n - 1} \Delta (r_{n - 1} \Delta y_{n - 1} )) = f(n,y_n \Delta y_{n - 1} ) + g(n,y_n \Delta y_{n - 1} ),
$
\Delta (p_{n - 1} \Delta (r_{n - 1} \Delta y_{n - 1} )) = f(n,y_n \Delta y_{n - 1} ) + g(n,y_n \Delta y_{n - 1} ),
相似文献
11.
We study the behavior of positive solutions of the following Dirichlet problem
|
$
\left \{ {ll} -\Delta_{p}u=\lambda u^{s-1}+u^{q-1} &\quad {\rm in}
\enspace \Omega \\ u_{\mid\partial \Omega}=0
\right. $
\left \{ \begin{array}{ll} -\Delta_{p}u=\lambda u^{s-1}+u^{q-1} &\quad {\rm in}
\enspace \Omega \\ u_{\mid\partial \Omega}=0 \end{array}
\right. 相似文献
12.
Let $
\mathbb{B}
$
\mathbb{B}
be the unit ball in ℂ
n
and let H($
\mathbb{B}
$
\mathbb{B}
) be the space of all holomorphic functions on $
\mathbb{B}
$
\mathbb{B}
. We introduce the following integral-type operator on H($
\mathbb{B}
$
\mathbb{B}
):
|
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
相似文献
13.
Let
J:\mathbb R ? \mathbb RJ:\mathbb{R} \to \mathbb{R}
be a nonnegative, smooth compactly supported function such that
ò \mathbbR J( r) dr = 1. \int_\mathbb{R} {J(r)dr = 1.}
We consider the nonlocal diffusion problem
|
$
u_t (x,t) = \int_\mathbb{R} {J\left( {\frac{{x - y}}
{{u(y,t)}}} \right)dy - u(x,t){\text{ in }}\mathbb{R} \times [0,\infty )}
$
u_t (x,t) = \int_\mathbb{R} {J\left( {\frac{{x - y}}
{{u(y,t)}}} \right)dy - u(x,t){\text{ in }}\mathbb{R} \times [0,\infty )}
相似文献
14.
We consider the properties on solutions of some q-difference equations of the form ∑ n j=0 aj（z）f（qj z）=an＋1（z）, where a0（z）,..., an＋1（z） are meromorphic functions, a0（z）an（z） ≠ 0 and q ∈ C such that 0 〈 ｜q｜ ≤ 1. We give estimates on the upper bound for the length of the gap in the power series of entire solutions of （＊） when the coefficients a0（z）,..., an＋1（z） are polynomials and 0 〈 ｜q｜ 〈 1. For some special cases, we give estimates of growth of f（z）. And we also show that the case 0 〈 ｜q｜ 〈 1 is different from the case ｜q｜=1. 相似文献
15.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φ x of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
16.
In a loaded Jacobi space with the inner product
|
$
\left\langle {f,g} \right\rangle = \frac{{\Gamma (\alpha + \beta + 2)}}{{2^{\alpha + \beta + 1} \Gamma (\alpha + 1)\Gamma (\beta + 1)}}\smallint _{ - 1}^1 fg(1 - x)^\alpha (1 + x)^\beta dx + Lf(1)g(1) + Mf( - 1)g( - 1)(L,M \ge 0)
$
\left\langle {f,g} \right\rangle = \frac{{\Gamma (\alpha + \beta + 2)}}{{2^{\alpha + \beta + 1} \Gamma (\alpha + 1)\Gamma (\beta + 1)}}\smallint _{ - 1}^1 fg(1 - x)^\alpha (1 + x)^\beta dx + Lf(1)g(1) + Mf( - 1)g( - 1)(L,M \ge 0)
相似文献
17.
Imaginary powers associated to the Laguerre differential operator $
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
$
L_\alpha = - \Delta + |x|^2 + \sum _{i = 1}^d \frac{1}
{{x_i^2 }}(\alpha _i^2 - 1/4)
are investigated. It is proved that for every multi-index α = (α 1,...α
d
) such that α
i
≧ −1/2, α
i
∉ (−1/2, 1/2), the imaginary powers $
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
$
\mathcal{L}_\alpha ^{ - i\gamma } ,\gamma \in \mathbb{R}
, of a self-adjoint extension of L
α, are Calderón-Zygmund operators. Consequently, mapping properties of $
\mathcal{L}_\alpha ^{ - i\gamma }
$
\mathcal{L}_\alpha ^{ - i\gamma }
follow by the general theory. 相似文献
18.
The paper is devoted to study the asymptotic behaviour of zeros z
n
of an entire function of Mittag-Leffler's type |
0,\mu \in C.}}} \right. \kern-\nulldelimiterspace} {\Gamma (\mu + {n \mathord{\left/ {\vphantom {n \rho }} \right. \kern-\nulldelimiterspace} \rho }),\rho > 0,\mu \in C.}}}$$
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19.
The following classes of functions analytic in the unit disk are considered: and where
is the Nevanlinna characteristic and
is a properly changing positive function on (0,1]. Necessary and sufficient conditions on
are established under which the classes
and
are invariant under the operators of differentiation and integration. Bibliography: 7 titles. 相似文献
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