共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper. 相似文献
2.
Let {X, X_k : k ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution F. In this paper, the authors establish some results on the local precise large and moderate deviation probabilities for partial sums S_n =sum from i=1 to n(X_i) in a unified form in which X may be a random variable of an arbitrary type,which state that under some suitable conditions, for some constants T 0, a and τ 1/2and for every fixed γ 0, the relation P(S_n- na ∈(x, x + T ]) ~nF((x + a, x + a + T ]) holds uniformly for all x ≥γn~τ as n→∞, that is, P(Sn- na ∈(x, x + T ]) lim sup- 1 = 0.n→+∞x≥γnτnF((x + a, x + a + T ])The authors also discuss the case where X has an infinite mean. 相似文献
3.
Han Yongsheng 《数学年刊B辑(英文版)》1983,4(1):15-20
A measure μ is called Carleson measure,iff the condition of Carleson type μ(Q~*)≤C|Q|~α(a≥1)is satisfied,where C is a constant independent of the cube Q with edge lengthq>0 in R~n and Q~*={(y,t)∈R_+~(+1)|y∈Q,0相似文献
4.
Yongtao Jing & Zhaoli Liu 《数学研究》2015,48(3):290-305
Let $1
0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results. 相似文献
5.
Tongzhu LI 《数学年刊B辑(英文版)》2017,38(5):1131-1144
Let x : M~n→ S~(n+1) be an immersed hypersurface in the(n + 1)-dimensional sphere S~(n+1). If, for any points p, q ∈ Mn, there exists a Mbius transformation φ :S~(n+1)→ S~(n+1) such that φox(Mn~) = x(M~n) and φ ox(p) = x(q), then the hypersurface is called a Mbius homogeneous hypersurface. In this paper, the Mbius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a Mbius transformation. 相似文献
6.
Existence and concentration result for Kirchhoff equations with critical exponent and Hartree nonlinearity
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This paper is concerned with the following Kirchhoff-type equations
$$
\left\{
\begin{array}{ll}
\displaystyle
-\big(\varepsilon^{2}a+\varepsilon b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\mathrm{d}x\big)\Delta u
+ V(x)u+\mu\phi |u|^{p-2}u=f(x,u), &\quad \mbox{ in }\mathbb{R}^{3},\(-\Delta)^{\frac{\alpha}{2}} \phi=\mu|u|^{p},~u>0, &\quad \mbox{ in }\mathbb{R}^{3},\\end{array}
\right.
$$
where $f(x,u)=\lambda K(x)|u|^{q-2}u+Q(x)|u|^{4}u$, $a>0,~b,~\mu\geq0$ are constants, $\alpha\in(0,3)$, $p\in[2,3),~q\in[2p,6)$ and $\varepsilon,~\lambda>0$ are parameters. Under some mild conditions on $V(x),~K(x)$ and $Q(x)$, we prove that the above system possesses a ground state solution $u_{\varepsilon}$ with exponential decay at infinity for $\lambda>0$ and $\varepsilon$ small enough. Furthermore, $u_{\varepsilon}$ concentrates around a global minimum point of $V(x)$ as $\varepsilon\rightarrow0$. The methods used here are based on minimax theorems and the concentration-compactness principle of Lions. Our results generalize and improve those in Liu and Guo (Z Angew Math Phys 66: 747-769, 2015), Zhao and Zhao (Nonlinear Anal 70: 2150-2164, 2009) and some other related literature. 相似文献
7.
带一类时滞项的生物种群扩散模型的行波解 总被引:1,自引:0,他引:1
本文利用Schauder不动点理论证明了微分积分方程组行波解u(x,t)=U(z),w(x,t)=W(z),z=xγ-ct的存在性.这个方程组描述了一类在植物上繁殖,且靠飞行在空中扩散的生物种群扩散过程.特别当时滞项,中积分核K(t)(反映种群繁殖模式)属于L1(0,∞)时,本文得到极限值W(-∞)(表示最终植物上种群密度)小于M.这个结论较符合生物实际. 相似文献
8.
Zhu Rujin 《数学年刊B辑(英文版)》1982,3(2):159-168
In this paper, we provide the existence theorem for solutions of general boundary value problem of quasi-linear second order elliptic differential equations in the following form:
$\[\sum\limits_{i,j = 1}^n {({a_{ij}}(x,u)\frac{{\partial u}}{{\partial {x_j}}}) + a(x,u,{u_{{x_k}}}),{\rm{ }}in} {\rm{ }}\Omega \]$,
$\[\alpha (x,u)\frac{{\partial u}}{{\partial \gamma }} + \beta (x,u) = 0,{\rm{ on }}\partial \Omega \]$,
where \alpha(x, u) \geq 0,\alpha_u(x, u) \leq 0 and \gamma is some direction, defining on $\[\partial \Omega \]$. 相似文献
9.
Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities
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In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation
$$
\left\{
- \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3,
\right.
$$
where $1
相似文献
10.
We investigate the existence of the global weak solution to the coupled Chemotaxisfluid system ■in a bounded smooth domain ??R~2. Here, r≥0 and μ 0 are given constants,?Φ∈L~∞(?) and g∈L~2((0, T); L_σ~2(?)) are prescribed functions. We obtain the local existence of the weak solution of the system by using the Schauder fixed point theorem. Furthermore, we study the regularity estimate of this system. Utilizing the regularity estimates, we obtain that the coupled Chemotaxis-fluid system with the initial-boundary value problem possesses a global weak solution. 相似文献
11.
Benboubker Mohamed Badr Hjiaj Hassan OUARO Stanislas 《Journal of Applied Analysis & Computation》2014,4(3):245-270
In this work, we give an existence result of entropy solutions for nonlinear anisotropic elliptic equation of the type $$- \mbox{div} \big( a(x,u,\nabla u)\big)+ g(x,u,\nabla u) + |u|^{p_{0}(x)-2}u = f-\mbox{div} \phi(u),\quad \mbox{ in } \Omega,$$ where $-\mbox{div}\big(a(x,u,\nabla u)\big)$ is a Leray-Lions operator, $\phi \in C^{0}(I\!\!R,I\!\!R^{N})$. The function $g(x,u,\nabla u)$ is a nonlinear lower order term with natural growth with respect to $|\nabla u|$, satisfying the sign condition and the datum $f$ belongs to $L^1(\Omega)$. 相似文献
12.
应用锥压缩锥拉伸不动点定理和Leray-Schauder 抉择定理研究了一类具有P-Laplace算子的奇异离散边值问题$$\left\{\begin{array}{l}\Delta[\phi (\Delta x(i-1))]+ q_{1}(i)f_{1}(i,x(i),y(i))=0, ~~~i\in \{1,2,...,T\}\\\Delta[\phi (\Delta y(i-1))]+ q_{2}(i)f_{2}(i,x(i),y(i))=0,\\x(0)=x(T+1)=y(0)=y(T+1)=0,\end{array}\right.$$的单一和多重正解的存在性,其中$\phi(s) = |s|^{p-2}s, ~p>1$,非线性项$f_{k}(i,x,y)(k=1,2)$在$(x,y)=(0,0)$具有奇性. 相似文献
13.
Gao Ruxi 《数学年刊B辑(英文版)》1983,4(3):293-298
This paper deals with the following mixed problem for Quasilinear hyperbolic equationsThe M order uniformly valid asymptotic solutions are obtained and there errors areestimated. 相似文献
14.
Wang Zhicheng 《数学年刊B辑(英文版)》1991,12(3):243-254
Consider the higher-order neutral delay differential equationd~t/dt~n(x(t)+sum from i=1 to lp_ix(t-τ_i)-sum from j=1 to mr_jx(t-ρ_j))+sum from k=1 to Nq_kx(t-u_k)=0,(A)where the coefficients and the delays are nonnegative constants with n≥2 even. Then anecessary and sufficient condition for the oscillation of (A) is that the characteristicequationλ~n+λ~nsum from i=1 to lp_ie~(-λτ_i-λ~n)sum from j=1 to mr_je~(-λρ_j)+sum from k=1 to Nq_ke~(-λρ_k)=0has no real roots. 相似文献
15.
In this paper, we study a system of Schr\"odinger-Poisson equation
\[
\left\{
\begin{array}{c}
-\Delta u+a(x)u+K(x)\phi u=|u|^{p-2}u,\quad \quad \quad \ \ \ \ \ \ x\in \mathbb{R}^3, \-\Delta \phi=K(x)u^2,\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ x\in \mathbb{R}^3,
\end{array}
\right.
\]
where $p\in (4,6)$ and $ K\geq (\not\equiv) 0$. Under some suitable decay assumptions but without any symmetry property on $a$ and $K$, we obtain infinitely many solutions of this system. 相似文献
16.
Consider initial value probiom v_t-u_x=0, u_t+p(v)_x=0, (E), v(x, 0)=v_0(x), u(x, 0)=u_0(x), (I), where A≥0, p(v)=K~2v~(-γ), K>0, 0<γ<3. As 0<γ≤1, the authors give a sufficient condition for that (E), (I) to have a unique global smooth solution, As 1≤γ<3, a necessary condition is given for that. 相似文献
17.
Huang Wenzhang 《数学年刊B辑(英文版)》1984,5(4):711-720
In this paper, the author considers the two-dimensional delay systems
$$\[\mathop x\limits^ \cdot (t) = Ax(t) + Bx(t - r),A,B \in {R^{2 \times 2}},x \in {R^2},r = const \ge 0\]$$
and gives the necessary and sifficient conditions under which where exists a simple type of positive definite Liapunov functional
$$\[V(\varphi ) \buildrel \Delta \over = {\varphi ^''}(0){T_\varphi }(0) + \int_{ - \tau }^0 {{\varphi ^''}(\theta )E\varphi (\theta )d\theta } \]$$
and $\[\alpha (s)\]$(where T , E are positive definite 2x2 matrices, $\[\varphi \in C([ - \tau ,0],{R^n})\]$, "." stands for transpose, $\[\alpha (s)\]$ is continuous and $\[\alpha (0) = 0,\alpha (s) > 0,s > 0\]$. such that $\[{V_{(*)}}(\varphi ) \le - \alpha (\left| {\varphi (0)} \right|).\]$. 相似文献
18.
B. Abdellaoui E. Colorado I. Peral 《Calculus of Variations and Partial Differential Equations》2005,23(3):327-345
For 1 < p < N and
we obtain the following improved Hardy-Sobolev Inequalities
where 1 < q < p and
if
,
if
, for some positive constant
.
Also we give an alternative proof of the optimal improved inequality for p = 2 by Wang-Willem in [16].
Received: 2 February 2004, Accepted: 12 July 2004, Published online: 3 September 2004
Mathematics Subject Classification (2000):
35J20, 35P05, 35R05, 46E30, 46E35
Partially supported by Project BFM2001-0183 相似文献
19.
A time fractional functional differential equation driven by the fractional Brownian motion
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Let $B^H$ be a fractional Brownian motion with Hurst index $H>\frac12$. In this paper, we prove the global existence and uniqueness of the equation
$$
\begin{cases}
^CD_t^{\gamma}x(t)=f(x_t)+G(x_t)\frac{d}{dt}B^H(t),\ \ \ \ &t\in(0,T], \x(t)=\eta(t), \ \ \ \ \ &t\in[-r,0],
\end{cases}
$$
where $\max\{H,2-2H\}<\gamma<1$, $^CD_t^{\gamma}$ is the Caputo derivative, and $x_t\in \mathcal{C}_r=\mathcal{C}([-r,0],\mathbb{R})$ with $x_t(u)=x(t+u),u\in[-r,0]$. We also study the dependence of the solution on the initial condition. 相似文献
20.