共查询到20条相似文献，搜索用时 51 毫秒
1.
With the aids of variational method and concentration-compactness principle, infinitely many solutions are obtained for a class of fourth order elliptic equations with singular potential Δ^2u=μ｜u｜^2＊＊（s）-2u/｜x｜^s＋λk（x）｜u｜^r-2 u, u∈H^2,2（R^N） （P） 相似文献
2.
Let→b=(b1,b2,…,bm),bi∈∧βi(Rn),1≤I≤m,βi＞0,m∑I=1βi=β,0＜β＜1,μΩ→b(f)(x)=(∫∞0|F→b,t(f)(x)|2dt/t3)1/2,F→b,t(f)(x)=∫|x-y|≤t Ω(x,x-y)/|x-y|n-1 mΠi=1[bi(x)-bi(y)dy.We consider the boundedness of μΩ,→b on Hardy type space Hp→b(Rn). 相似文献
3.
We characterize the group Aut
for the symmetrized bidisc
Both authors were supported in part by KBN grant no. 5 P03A 033 21 and by DFG grant no. 227/8-1. 相似文献
4.
We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball
For a function u which is lower semi-continuous on
we give necessary and sufficient conditions in order that there exists a holomorphic function f ∈
such that . 相似文献
5.
In this paper we consider the bifurcation problem -div A（x, u）=λa（x）｜u｜^p-2u＋f（x,u,λ） in Ω with p 〉 1.Under some proper assumptions on A（x,ξ）,a（x） and f（x,u,λ）,we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A（x, u）=λa（x）｜u｜^p-2u. 相似文献
6.
Let Ω be an open bounded domain in ℝ N( N ≥ 3) and
. We are concerned with two kinds of critical elliptic problems. The first one is where 0 ∈ Ω,
, 2 < m < 2* and λ > 0. By using the fountain theorem and concentration estimates, if N ≥ 7 and θ > 0, we establish the existence of infinitely many solutions for the following regularization of (*) with small number ϵ > 0 Then if θ > 0 is suitably small, we obtain many solutions for problem (*) by taking the process of approximation.
The second problem is where q ∈ (0, 1), t > 0. By using similar methods as in (*), we prove that if N ≥ 7,
and t > 0, there exist infinitely many solutions with positive energy. In particular, we give a positive answer to one open problem
proposed by Ambrosetti, Brezis and Cerami [1]. 相似文献
7.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems
|
$\left\{ \begin{gathered}
- \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
- \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
\end{gathered} \right.$\left\{ \begin{gathered}
- \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
- \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\
\end{gathered} \right. 相似文献
8.
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
9.
It is proved that if P( D) is a regular, almost hypoelliptic operator and
|
$
L_{2,\delta } = \left\{ {u:\left\| u \right\|_{2,\delta } = \left[ {\int {\left( {|u(x)|e^{ - \delta |x|} } \right)^2 dx} } \right]^{1/2} < \infty } \right\},\delta > 0,
$
L_{2,\delta } = \left\{ {u:\left\| u \right\|_{2,\delta } = \left[ {\int {\left( {|u(x)|e^{ - \delta |x|} } \right)^2 dx} } \right]^{1/2} < \infty } \right\},\delta > 0,
相似文献
10.
Let {A, B} and {C, D} be diagonalizable pairs of order n, i.e., there exist invertible matrices P, Q and X, Ysuchthat A = P∧Q, B = PΩQ, C =XГY, D= X△Y, where ∧ = diag（α1, α2, …, αn）, Ω= diag（βl, β2, …βn）, Г=diag（γ1,γ2,…,γn）, △=diag（δl,δ2,…,δn）. Let ρ（（α,β）, （γ,δ））=｜αδ-βγ｜/√｜α｜^2＋｜β｜^2√｜γ｜^2＋｜δ｜^2.In this paper, it will be proved that there is a permutation τ of {1,2,... ,n} such that n∑i=1[ρ（（αi,βi）,（γτ（i）,δτ（i）））]^2≤n[1-1/κ^2（Y）κ^2（Q）（1-d2F（Z,W）/n）], where κ（Y） = ｜｜Y｜｜2｜｜Y^-1｜｜2,Z= （A,B）,W= （C, D） and dF（Z,W） = 1/√2｜｜Pz＊ -Pw＊｜｜F. 相似文献
11.
Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ
2
, and let
be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:
, where
with
is the scalar product in ℝ
3
and
is the external loading per unit surface. We take into account the fact that an infinite amount of energy is required to compress
a finite surface of the plate into zero surface, i.e.,
Mathematics Subject Classification (2000) 49J45 相似文献
12.
Let Ω be an open bounded domain in with smooth boundary . We are concerned with the critical Neumann problem
where and Q( x) is a positive continuous function on . Using Moser iteration, we give an asymptotic characterization of solutions for (*) at the origin. Under some conditions
on Q, μ, we, by means of a variational method, prove that there exists such that for every , problem (*) has a positive solution and a pair of sign-changing solutions. 相似文献
14.
In this paper, we consider a linearly elastic shell, i.e. a three-dimensional linearly elastic body with a small thickness denoted by 2ε, which is clamped along its part of the lateral boundary and subjected to the regular loads. In the linear case, one can use the two-dimensional models of Ciarlet or Koiter to calculate the displacement for the shell. Some error estimates between the approximate solution of these models and the three-dimensional displacement vector field of a flexural or membrane shell have been obtained. Here we give a new model for a linear and nonlinear shell, prove that there exists a unique solution U of the two-dimensional variational problem and construct a three-dimensional approximate solutions UKT(x,ξ) in terms of U: We also provide the error estimates between our model and the three-dimensional displacement vector field :‖u-UKT‖1,Ω≤C∈r,r=3/2, an elliptic membrane, r = 1/2, a general membrane, where C is a constant dependent only upon the data‖u‖3,Ω,‖UKT‖3,Ω,θ. 相似文献
15.
We study the Γ-convergence of the following functional ( p > 2)
|
$F_{\varepsilon}(u):=\varepsilon^{p-2}\int\limits_{\Omega}
|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\varepsilon^{\frac{p-2}{p-1}}}
\int\limits_{\Omega}
W(u) d(x,\partial \Omega)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrt{\varepsilon}}
\int\limits_{\partial\Omega}
V(Tu)d\mathcal{H}^2,$F_{\varepsilon}(u):=\varepsilon^{p-2}\int\limits_{\Omega}
|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\varepsilon^{\frac{p-2}{p-1}}}
\int\limits_{\Omega}
W(u) d(x,\partial \Omega)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrt{\varepsilon}}
\int\limits_{\partial\Omega}
V(Tu)d\mathcal{H}^2, 相似文献
16.
For positive integers with a
r
= 2, the multiple zeta value or r-fold Euler sum is defined as [2]
. There is a celebrated sum formula [6, 10] among multiple zeta values as ,
where range over all positive integers with in the summation.
In this paper, we shall prove the so called restricted sum formula [4]. Namely, for all positive integers m and q with m ≥ q and a nonnegative integer p, that
. We prove the assertion by new expressions of multiple zeta values in terms of Drinfeld integrals.
This work was supported by the Department of Mathematics, National Chung Cheng University and by the National Science Council
of Taiwan, Republic of China. 相似文献
17.
We develop structural formulas satisfied by some families of orthogonal matrix polynomials of size 2 × 2 satisfying second-order
differential equations with polynomial coefficients. We consider here three one-parametric families of weight matrices, namely,
and
and their corresponding orthogonal polynomials. We also show that the orthogonal polynomials with respect to the second family
are eigenfunctions of two linearly independent second-order differential operators. 相似文献
18.
In what follows, $C$ is the space of
-periodic continuous functions; P is a seminorm defined on C, shift-invariant, and majorized by the uniform norm;
is the mth modulus of continuity of a function f with step h and calculated with respect to P;
,
(
),
, ,
Theorem 1.
Let
. Then
For some values of
and seminorms related to best approximations by trigonometric polynomials and splines in the uniform and integral metrics, the inequalities are sharp. Bibliography: 6 titles. 相似文献
19.
A detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems (PPEP)
|
$ \left(\sum_{\ell=0}^d A_{\ell}
\lambda^{\ell}
\right)x=0, \quad A_{d-\ell}=\varepsilon A_{\ell}^{\star}
\quad{\rm for}\,\ell=0,1,\ldots,\lfloor d/2\rfloor, $ \left(\sum_{\ell=0}^d A_{\ell}
\lambda^{\ell}
\right)x=0, \quad A_{d-\ell}=\varepsilon A_{\ell}^{\star}
\quad{\rm for}\,\ell=0,1,\ldots,\lfloor d/2\rfloor, 相似文献
20.
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
and
are studied and some new multiplicity results of solutions for systems (1.λ) and (2.λ) are obtained. Moreover, by using the
KKM principle we give also two new existence results of solutions for systems (1.1) and (2.1).
This Work is supported in part by the National Natural Science Foundation of China (10561011). 相似文献
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