共查询到20条相似文献，搜索用时 46 毫秒
1.
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
2.
If P(z) is a polynomial of degree n which does not vanish in |z| 1,then it is recently proved by Rather [Jour.Ineq.Pure and Appl.Math.,9 (2008),Issue 4,Art.103] that for every γ 0 and every real or complex number α with |α|≥ 1,{∫02π |D α P(e iθ)| γ dθ}1/γ≤ n(|α| + 1)C γ{∫02π|P(eiθ)| γ dθ}1/γ,C γ ={1/2π∫0 2π|1+eiβ|γdβ}-1/γ,where D α P(z) denotes the polar derivative of P(z) with respect to α.In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J.Approx.Theory,54 (1988),306-313] as a special case. 相似文献
3.
Considering the positive d-dimensional lattice point Z
+
d
( d ≥ 2) with partial ordering ≤, let { X
k: k ∈ Z
+
d
} be i.i.d. random variables taking values in a real separable Hilbert space ( H, ‖ · ‖) with mean zero and covariance operator Σ, and set $
S_n = \sum\limits_{k \leqslant n} {X_k }
$
S_n = \sum\limits_{k \leqslant n} {X_k }
, n ∈ Z
+
d
. Let σ
i
2, i ≥ 1, be the eigenvalues of Σ arranged in the non-increasing order and taking into account the multiplicities. Let l be the dimension of the corresponding eigenspace, and denote the largest eigenvalue of Σ by σ
2. Let log x = ln( x ∨ e), x ≥ 0. This paper studies the convergence rates for $
\sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}} P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt {2\left| n \right|\log \log \left| n \right|} } \right)
$
\sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}} P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt {2\left| n \right|\log \log \left| n \right|} } \right)
. We show that when l ≥ 2 and b > − l/2, E[‖ X‖ 2(log ‖ X‖)
d−2(log log ‖ X‖)
b+4] < ∞ implies $
\begin{gathered}
\mathop {\lim }\limits_{\varepsilon \searrow \sqrt {d - 1} } (\varepsilon ^2 - d + 1)^{b + l/2} \sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt 2 \left| n \right|\log \log \left| n \right|} \right)} \hfill \\
= \frac{{K(\Sigma )(d - 1)^{\frac{{l - 2}}
{2}} \Gamma (b + l/2)}}
{{\Gamma (l/2)(d - 1)!}} \hfill \\
\end{gathered}
$
\begin{gathered}
\mathop {\lim }\limits_{\varepsilon \searrow \sqrt {d - 1} } (\varepsilon ^2 - d + 1)^{b + l/2} \sum\limits_n {\frac{{\left( {\log \log \left| n \right|} \right)^b }}
{{\left| n \right|\log \left| n \right|}}P\left( {\left\| {S_n } \right\| \geqslant \sigma \varepsilon \sqrt 2 \left| n \right|\log \log \left| n \right|} \right)} \hfill \\
= \frac{{K(\Sigma )(d - 1)^{\frac{{l - 2}}
{2}} \Gamma (b + l/2)}}
{{\Gamma (l/2)(d - 1)!}} \hfill \\
\end{gathered}
, where Γ(·) is the Gamma function and $
\prod\limits_{i = l + 1}^\infty {((\sigma ^2 - \sigma _i^2 )/\sigma ^2 )^{ - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} }
$
\prod\limits_{i = l + 1}^\infty {((\sigma ^2 - \sigma _i^2 )/\sigma ^2 )^{ - {1 \mathord{\left/
{\vphantom {1 2}} \right.
\kern-\nulldelimiterspace} 2}} }
. 相似文献
4.
Using the Leggett-Williams fixed point theorem,we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u(t)+g(t)f(t,u(t))=0,0 相似文献
5.
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects： {ψt=-（1-α）ψ-θx＋αψxx, θt=-（1-α）θ＋νψx＋（ψθ）x＋αθxx（E） with initial data （ψ,θ）（x,0）=（ψ0（x）,θ0（x））→（ψ±,θ±）as x→±∞ where α and ν are positive constants such that α 〈 1, ν 〈 4α（1 - α）. Under the assumption that ｜ψ＋ - ψ-｜ ＋ ｜θ＋ - θ-｜ is sufficiently small, we show the global existence of the solutions to Cauchy problem （E） and （I） if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method. 相似文献
6.
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation
|
$
\left\{ \begin{gathered}
x'(t) = f(t,x(t),x(\alpha _1 (t)),...,x(\alpha _n (t)))fora.e.t \in [0,T], \hfill \\
\Delta x(t_k ) = I_k (x(t_k )),k = 1,...,m, \hfill \\
x(0) = x(T). \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
x'(t) = f(t,x(t),x(\alpha _1 (t)),...,x(\alpha _n (t)))fora.e.t \in [0,T], \hfill \\
\Delta x(t_k ) = I_k (x(t_k )),k = 1,...,m, \hfill \\
x(0) = x(T). \hfill \\
\end{gathered} \right.
相似文献
7.
This paper is devoted to the study of the period function for a class of reversible quadratic system
|
$
\begin{gathered}
\dot x = - 2xy, \hfill \\
\dot y = k - 1 - 2kx + \left( {k + 1} \right)x^2 - \tfrac{1}
{2}y^2 . \hfill \\
\end{gathered}
$
\begin{gathered}
\dot x = - 2xy, \hfill \\
\dot y = k - 1 - 2kx + \left( {k + 1} \right)x^2 - \tfrac{1}
{2}y^2 . \hfill \\
\end{gathered}
相似文献
8.
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
|
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
相似文献
9.
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
10.
we study an initial-boundary-value problem for the ＂good＂ Boussinesq equation on the half line {δt^2u-δx^2u＋δx^4u＋δx^2u^2=0,t〉0,x〉0. u（0,t）=h1（t）,δx^2u（0,t） =δth2（t）, u（x,0）=f（x）,δtu（x,0）=δxh（x）. The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data （f, h, h1, h2） belong to the product space H^5（R^＋）×H^s-1（R^＋）×H^s/2＋1/4（R^＋）×H^s/2＋1/4（R^＋） 1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered. 相似文献
11.
Let u = ( u
n
) be a sequence of real numbers whose generator sequence is Cesàro summable to a finite number. We prove that ( u
n
) is slowly oscillating if the sequence of Cesàro means of ( ω
n
(m−1)( u)) is increasing and the following two conditions are hold:
|
$\begin{gathered}
\left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\
\left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\
\end{gathered}$\begin{gathered}
\left( {\lambda - 1} \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{\left[ {\lambda n} \right] - n}}\sum\limits_{k = n + 1}^{\left[ {\lambda n} \right]} {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ + , q > 1, \hfill \\
\left( {1 - \lambda } \right)\mathop {\lim \sup }\limits_n \left( {\frac{1}
{{n - \left[ {\lambda n} \right]}}\sum\limits_{k = \left[ {\lambda n} \right] + 1}^n {\left( {\omega _k^{\left( m \right)} \left( u \right)} \right)^q } } \right)^{\frac{1}
{q}} = o\left( 1 \right), \lambda \to 1^ - , q > 1, \hfill \\
\end{gathered} 相似文献
12.
The initial boundary value problem
|
$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array} 相似文献
13.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
|
$
\left\{ \begin{gathered}
u_t - u_{xx} = f\left( u \right), x \in \left( {0,1} \right), t \in \left( {0,T} \right), \hfill \\
u\left( {0,t} \right) = 0, u_x \left( {1,t} \right) = 0, t \in \left( {0,T} \right), \hfill \\
u\left( {x,0} \right) = u_0 \left( x \right), x \in \left[ {0,1} \right], \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
u_t - u_{xx} = f\left( u \right), x \in \left( {0,1} \right), t \in \left( {0,T} \right), \hfill \\
u\left( {0,t} \right) = 0, u_x \left( {1,t} \right) = 0, t \in \left( {0,T} \right), \hfill \\
u\left( {x,0} \right) = u_0 \left( x \right), x \in \left[ {0,1} \right], \hfill \\
\end{gathered} \right.
相似文献
14.
This paper is concerned with a nonlocal hyperbolic system as follows utt = △u ＋ （∫Ωvdx ）^p for x∈R^N,t〉0 ,utt = △u ＋ （∫Ωvdx ）^q for x∈R^N,t〉0 ,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N,u（x,0）=u0（x）,ut（x,0）=u01（x） for x∈R^N, where 1≤ N ≤3, p ≥1, q ≥ 1 and pq 〉 1. Here the initial values are compactly supported and Ω belong to R^N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed. 相似文献
15.
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.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 272–302. 相似文献
16.
We consider the system
|
$\begin{gathered}
x_{k + 1} = A_k x_k + b_k u_k , \hfill \\
u_{k + 1} = m_k^* x_k ,k = 1,2,..., \hfill \\
\end{gathered}
$\begin{gathered}
x_{k + 1} = A_k x_k + b_k u_k , \hfill \\
u_{k + 1} = m_k^* x_k ,k = 1,2,..., \hfill \\
\end{gathered}
相似文献
17.
In this paper we deal with the four-point singular boundary value problem
|
$
\left\{ \begin{gathered}
(\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\
u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
(\phi _p (u'(t)))' + q(t)f(t,u(t),u'(t),u'(t)) = 0,t \in (0,1), \hfill \\
u'(0) - \alpha u(\xi ) = 0,u'(1) + \beta u(\eta ) = 0, \hfill \\
\end{gathered} \right.
相似文献
18.
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1＋a（1/√1＋a-ε）b＋1 ∑n=1^∞（logn）^a（loglogn）^b/nP{max κ≤n｜Sκ｜≤√σ^2π^2n/8loglogn（ε＋an）}=4/π（1/2（1＋a）^3/2）^b＋1 Г（b＋1）,whenever an = o（1/log log n）. The author obtains the sufficient and necessary conditions for this kind of results to hold. 相似文献
19.
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
20.
§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
|
|
| | | | | | | | |
