共查询到20条相似文献，搜索用时 31 毫秒
1.
Let X be a symmetric stable process of index α, 0<α<2, in Rd, let μ be a (signed) Radon measure on Rd belonging to the Kato class Kd, α and let F be a Borel function on Rd×Rd satisfying certain conditions. Suppose that A
t
μ
is the continuous additive functional with μ as its Revuz measure and
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相似文献
2.
We study the local smoothness of solutions to the magnetohydrodynamic equations where Ω is a domain in ℝ 3, Q T = Ω × (−T, 0), v: Q T → ℝ 3 is the velocity, p: Q T → ℝ is the pressure, and H: Q T → ℝ 3 is the stress of the magnetic field. An analog of the known Caffarelli-Kohn-Nirenberg theorem is established. Conditions
of ε-regularity are derived. Bibliography: 8 titles.
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Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 3–13. 相似文献
3.
The combinatorial identity is established with the help of the differentiation of the convolution of some function with the sine function. Bibliography:
5 titles.
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Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 65–67. 相似文献
4.
Let Ω 1, Ω 2 ⊂ ℝ ν be compact sets. In the Hilbert space L
2(Ω 1 × Ω 2), we study the spectral properties of selfadjoint partially integral operators T
1, T
2, and T
1 + T
2, with
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$
\begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered}
$
\begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered}
相似文献
5.
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
6.
It is proved that the boundary-value problem , has a solution, provided that the following conditions are fulfilled: , and, for ϕ(u) ≡ 0, the Galerkin method converges in the norm of the space H 1(a, b; a). Several theorems of a similar kind are presented. Bibliography: 4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 246–266. 相似文献
7.
Let Θ = ( θ
1, θ
2, θ
3) ∈ ℝ 3. Suppose that 1, θ
1, θ
2, θ
3 are linearly independent over ℤ. For Diophantine exponents
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$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered}$\begin{gathered}
\alpha (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\sup }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\}, \hfill \\
\beta (\Theta ) = sup\left\{ {\gamma > 0: \mathop {\lim }\limits_{t \to } \mathop {\inf }\limits_{ + \infty } t^\gamma \psi _\Theta (t) < + \infty } \right\} \hfill \\
\end{gathered} 相似文献
8.
We study the existence of nodal solutions of the m-point boundary value problem where η
i
∈ ℚ ( i = 1, 2, ..., m − 2) with 0 < η
1 < η
2 < ... < η
m−2 < 1, and α
i
∈ ℝ ( i = 1, 2, ..., m − 2) with α
i
> 0 and
< 1. We give conditions on the ratio f( s)/ s at infinity and zero that guarantee the existence of nodal solutions. The proofs of the main results are based on bifurcation
techniques. 相似文献
9.
Let Ω⊂ R
n
( n≥2) be a bounded open set; Q
T
=Ω×[0, T], S
T
=δΩ×[0, T], S
1, S
2 be the partial boundaries of Ω and S
1∪ S
2=δΩ, S
1∩ S
2=Φ. We denote Γ 1.T
= S
1×[0, T], Γ 2.T
= S
2×[0, T], and consider the problem
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相似文献
10.
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
By a constructive argument, we prove that for any k = 1, 2, • • •, if ε is small enough, then the above problem has positive a solution uε concentrating at k distinct points which tending to the boundary of Ω as ε goes to 0 +. 相似文献
11.
It is proved that the least energy solution of the BVP
, is a constant for all q ∈ (2; 2*] if Q ⊂ ℝ n (n ≥ 3) is a sufficiently thin cylinder. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 272–302. 相似文献
12.
In this paper, the sharp estimates of all homogeneous expansions for f are established, where f( z) = ( f
1( z), f
2( z), …, f
n
( z))′ is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in ℂ
n
and
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$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
相似文献
13.
§1 IntroductionAnvarovandLarinov[1]introducedthefollowingprey-predatorsystem:x(t)=x(t)[α-γy(t)-γ∫∞0K1(s)y(t-s)ds-∫∞0∫∞0R1(s,θ)y(t-s)y(t-θ)dθds],y(t)=y(t)[-β μx(t) μ∫∞0K2(s)x(t-s)ds ∫∞0∫∞0R2(s,θ)x(t-θ)x(t-s)dθds],(1)whereα,γ,βandμarepositiveconstants,Ki∈C([0,∞),(0,∞))andRi∈C([0,∞)×[0,∞),(0,∞)),i=1,2.Fortheecologicalsenseofsystem(1),wereferto[1,2]andrefer-encescitedtherein.Sincerealisticmodelsrequiretheinclusionoftheeffectofchangingen-vironment,itmot… 相似文献
14.
A graph G with p vertices and q edges, vertex set V( G) and edge set E( G), is said to be super vertex-graceful (in short SVG), if there exists a function pair ( f, f
+) where f is a bijection from V( G) onto P, f
+ is a bijection from E( G) onto Q, f
+(( u, v)) = f( u) + f( v) for any ( u, v) ∈ E( G), and
We determine here families of unicyclic graphs that are super vertex-graceful.
相似文献
15.
In problems of physics and engineering we often come across singular boundary value problems that cannot be solved by the
usual numerical methods. Special methods for solving such problems have been developed. These methods lead to banded systems,
linear and nonlinear depending upon the nature of the boundary value problem. In this paper a difference method based on nonuniform
mesh for a class of singular two-point boundary value problems of the form has been derived using Numerical Quadrature. It is shown to be order- h
2 convergent for all α ∈ (0, 1). The method is illustrated computationally by two numerical examples. 相似文献
16.
We consider the value distribution of Hurwitz zeta-functions
at the nontrivial zeros ϱ = β + iγ of the Riemann zeta-function ζ ( s):= ζ ( s, 1). Using the method of Conrey, Ghosh and Gonek we prove for fixed 0< α< 1 and H ≤ T that with some absolute constant C > 0 (a similar result was first proved by Fujii [4] under assumption of the Riemann hypothesis). It follows that
is an entire function if and only if α = 1/2 or α = l. Further, we prove for α ≠ 1/2, 1 the existence of zeros ϱ = β + iγ with T < γ ≤ T + T 3/4, 1/2 β ≤ 9/10 + ε and ζ(ϱ,α)≠0. 相似文献
17.
Given H≥0 and bounded convex curves α 1, ...,⇌ n, α in the plane z=0 bounding domains D 1, …, D n, D, respectively, with
if i ∈ j and with D i ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
α i, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献
18.
In this paper, for a second-order three-point boundary value problem u" f(t,u)=0, 0＜t＜l,au(0) - bu'(0) = 0, u(1) - αu(η) = 0,where η∈ (0, 1), a, b, α∈ R with a2 b2 ＞ 0, the existence of its nontrivial solution is studied.The conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given. 相似文献
20.
The authors study the existence of homoclinic type solutions for the following system of diffusion equations on R × RN:{■tu-xu + b ·▽xu + au + V(t,x)v = Hv(t,x,u,v),-■tv-xv-b·▽xv + av + V(t,x)u = Hu(t,x,u,v),where z =(u,v):R × RN → Rm × Rm,a > 0,b =(b1,···,bN) is a constant vector and V ∈ C(R × RN,R),H ∈ C1(R × RN × R2m,R).Under suitable conditions on V(t,x) and the nonlinearity for H(t,x,z),at least one non-stationary homoclinic solution with least energy is obtained. 相似文献
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