关于Young氏积分不等式的注记

The well-known inequality of W.H.Young may be written as abintegral from 0 to a(Φ(x)dx)+integral from 0 to b(ψ(x)dx),where a>0,b>0,and Φ(x)∈C(0,∞) increases strictly with x and Φ(0)=0, andΨ(x) is the inverse function so that Ψ(Ф(x)=Ф(Ψ(x))=x.An investigation intothe graphs of the functions y=Φ(x) and x=Ψ(y) reveals that     

HOMOGENIZATION FOR NONLINEAR SCHRODINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

We study the nonlinear Schrodinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iΨ_t + ΔΨ + φ(ωt)|Ψ|~αΨ+iζ(ωt)Ψ=0.Under some conditions,we show that as ω→∞,the solution Ψ_ω will locally converge to the solution of the averaged equation iΨ_t+ΔΨ + φ_|Ψ|~αΨ+iζoΨ=0 with the same initial condition in L~q((0,T),B_(r,2)~s)for all admissible pairs(q,r),where T ∈(0,T_(max)).We also show that if the dissipation coefficient ζo large enough,then,Ψ_ω is global if ω is sufficiently large and Ψ_ω converges toΨ in L~q((0,∞),B_(r,2)~s),for all admissible pairs(q,r).In particular,our results hold for both subcritical and critical nonlinearities.     

复超球上的完备度量

<正> 设 M 为单连通完备 Riemann 流形,有极点 O.如果对于每一线性等度:(?):M_0→M_0(M_0为 O 点的切空间),都有等度映射Φ:M→M,使得Φ(0)=0,Φ_*=(?),则称 M是模.如对任意的 X,X'∈M_0,‖X‖=‖X'‖,都存在一等度映射Ψ:M→M,使得Ψ(0)=0,Ψ_*X=X',则称 M 是弱模(见[1],p24).     

一类二次方程组的一个定理及其运用

定理　在方程组∑ni=1xi=A∑ni=1x2i=B中 ,A、B是实数 ,记Δ=n B-A2 .若 xi∈ R( i=1,2 ,… ,n) ,则Δ≥ 0 ,当且仅当x1 =x2 =… =xn=An时 Δ=0 .证明　 ∑1≤ i相似文献   

拟分布余弦函数

设X是Banach空间;本文研究了X上定义的拟分布余弦函数:2G（φ）G（Ψ）=G（φ＊Ψ）+G（φ（?）Ψ）,（?）φ,Ψ∈D;在D上引入了一种新的运算“（?）”并研究了拟分布余弦函数、积分余弦算子函数和二阶抽象Cauchy问题之间的关系.     

C_(p,q)~(s+α)-forms Solution of _b-equ ation and Its L_(p,q)~s Estimates

§ 1.　Introduction　　TheinhomogeneoustangentialCauchy Riemannoperators,or b complex ,onthebound aryofadomainDinCn(n ≥ 2 ) ,hasplayedanimportantroleinthestudyofboundaryvaluesofholomorphicfunctionsandholomorphicextensioninCn(examplesseeKOHNandROSSI[3] ,AndrettiandHILL [4] ) .In 1 977,HENKIN [1 ]wasfirstlyobservedthat,if b equa tions bu =fon Dissolvable ,the (p ,1 ) form ,f ,0≤ p≤ 2 ,mustsatisfythecompatibilitycondition∫ Df∧Ψ =0forall b closed (2 p ,0 ) formsΨonDinwhich…     

一维Chemotaxis模型双曲组的解的存在性及其抛物组的行波解

研究了一类简化的 Keller- Segel模型 pt=εpxx+ a( pwxw) x,wt=λpw- b w,x∈ R,t>0 ,按照 ε=0和 ε>0两种不同的情况模型进行讨论 .当 ε=0时 ,采用特征的方法 ,通过计算特征值与黎曼不等式 ,给出问题存在局部解且不可能有整体解的一个充分条件 .当 ε>0 ,给出了它的行波解的一个形式表达式 .     

一维奇异p-Laplace方程的上下解方法[英文]

本文讨论了一维奇异 p Laplace方程( φp( y′) )′+ q(t) f(t,y) =0 ,0 相似文献   

相伴于随机自相似分形的随机测度的强测度的收敛性(英文)

构造了随机自相似分形及其上的记忆函数,并得出了有关结论,在此基础上,我们可以定义一个随机概率测度dΦn(τ)=Kn(τ)dτ,Φn(τ)弱收敛于Φ,进一步可得到强测度序列Ψn(.)=EΦn(.),则{Ψn}弱收敛于Ψ=EΦ.     

非齐次粗糙核参数型Marcinkiewicz算子的H~p有界性

设Ω是球面上函数,b是径向函数,ρ是实部正的复数;设Ψ为C~2([0,∞))的递增凸函数,Ψ(0)=0.本文研究非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,b)~ρ,以及旋转曲面上的非齐次粗糙核参数型Marcinkiewicz算子μ_(Ω,Ψ,b)~ρ,给出非齐次粗糙核Ω和b的最小光滑性条件,建立算子μ_(Ω,b)~ρ和μ_(Ω,Ψ,b)~ρ在Hardy空间和弱Hardy空间上的有界性.本文结果推进了先前b≡1情形的已有工作.     

AF—代数的闭的Jordan理想

讨论AF-代数的闭的Jordan理想。我们证明了AF-代灵敏的一个闭的子集是其一Jordan理想的充分必要条件是它是一个结合理想。     

On the determination of the number of periodic (or closed) solutions of a scalar differential equation with convexity

It is well known that a scalar differential equation , where f(t,x) is continuous, T-periodic in t and weakly convex or concave in x has no, one or two T-periodic solutions or a connected band of T-periodic solutions. The last possibility can be excluded if f(t,x) is strictly convex or concave for some t in the period interval. In this paper we investigate how the actual number of T-periodic solutions for a given equation of this type in principle can be determined, if f(t,x) is also assumed to have a continuous derivative . It turns out that there are three cases. In each of these cases we indicate the monotonicity properties and the domain of values for the function P(ξ)=S(ξ)−ξ, where S(ξ) is the Poincaré successor function. From these informations the actual number of periodic solutions can be determined, since a zero of P(ξ) represents a periodic solution.     

一类拟线性常微分方程的多解

说明一类拟线性特征值问题有两个正解;一个大解,一个小解。同时本也证明小解是一个山路解当参数大时发展成为尖解。     

On a class of nonlinear elliptic equations with fast increasing weight and critical growth

We are concerned with the existence of rapidly decaying solutions for the equation

     

Solutions of the generalized Lennard-Jones system

In this paper, we study solution structures of the following generalized Lennard-Jones system in R~n,x=(-α/|x|~(α+2)+β/|x|~(β+2))x,with 0 α β. Considering periodic solutions with zero angular momentum, we prove that the corresponding problem degenerates to 1-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.     

Weak solutions for equations defined by accretive operators II: relaxation limits

In the first part of this paper we define solutions for certain nonlinear equations defined by accretive operators, “dissipative solution”. This kind of solution is equivalent to the viscosity solutions for Hamilton-Jacobi equations and to the entropy solutions for conservation laws.In this paper we use dissipative solutions to obtain several relaxation limits for systems of semilinear transport equations and quasilinear conservation laws. These converge to diffusion second-order equations and in one case to a single conservation law. The relaxation limit is obtained using a version of the perturbed test function method to pass to the limit. This guarantees existence for the considered equations.     

On the existence of bounded noncontinuable solutions

This paper presents necessary and sufficient conditions for an n ‐th order differential equation to have a non‐continuable solution with finite limits of its derivatives up to the order l at the right‐hand end point of the interval of its definition, l ≤ n – 2 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)