具p-Laplacian算子型奇异方程组边值问题正解的存在性

本文讨论了一类具p-Laplacian算子型奇导方程组边值问题(φp(x'))'+α1(t),f(x(t),y(t))=0,(φp(y'))'+α2(t)g(x(t),y(t))=0,x(0)-β1x'(0)=0,x(1)+δ1x'(1)=0,y(0)-β2Y'(0)=0,y(1)+δ2y'(1)=0正解的存在性,其中φp(x)=|x|p-2x,p>1.通过使用不动点指数定理,在适当的条件下,建立了这类奇异方程组边值问题存在一个或者多个正解的充分条件.这些结果能用来研究椭圆型方程组边值问题径向对称解的存在性.     

二阶奇异微分方程边值问题的正解

利用上下解方法研究二阶奇异微分方程u″+f(t,u)=0在边界条件αu(0)-βu′(0)=0,γu(1)+δu′(1)=0下正解的存在性.允许f(t,u)在t=0,1处奇异.     

奇异sturm-Liouville特征值问题正解的全局分歧和存在性

本文研究了奇异Sturm-Liouville特征值问题{u'(t)+λa(t)f(u(t))=0,0t1,u(0)-βu'(0)=0,u(1)+γu'(1)=αu(η),其中λ0是参数,α,β,γ≥0,0≤η≤1;α∈C((0,1),(0,+∞))在t=0和/或t=1处可能有奇性,f∈C([0,+∞),(0,+∞)).文中首先给出了正解的一些精确的先验估计和渐近行为分析.再利用这些结果联合不动点指数定理证明了正解的全局存在性.一个关键的技术是利用连续统构造上下解.     

有关Sturm—Liouville条件下的四阶奇异边值问题正解的研究

获得如下四阶奇异边值问题{u^（4）（t）-λh（t）f（t,u（t））=0,t∈（0,1）,u（0）=u（1）=0,αu^·（0）-βu^·（0）=γu^·（1）＋δu^·（1）=0,正解的存在性定理，其中α,β,γ,δ≥0,α＋β＞0,δ＋γ＞0,ρ=αγ＋γβ＋δα＞0,参数λ＞0，h（t）∈C（0,1）and f∈（（0,1）×（0,＋∞））文中主要应用全连续算子的逼近技巧和延拓定理以及不动点指数理论．     

具有变号非线性项的奇异三点边值问题正解的存在性和不存在性

该文讨论奇异三点边值问题 y'(t)+a(t)f(t, y(t), y'(t))= 0, 0相似文献   

带p-Laplacian算子的四阶四点边值问题迭代解的存在性

考虑带p-Laplacian算子的四阶四点边值问题(φp(x″(t)))″=f(t,x(t),x″(t)),t∈[0,1],x(0)-αx′(0)=0,x(1)+βx′(1)=0,φp(x″(ξ))-γ(φp(x″(ξ)))′=0,φp(x″(η))+δ(φp(x″(η)))′=0,其中φp(s)=s p-2s,p>1;0<ξ,η<1;f∈C([0,1]×R2,R).通过建立上下解方法得到迭代解的存在性.     

具$p$-Laplacian 算子的多点边值问题迭代解的存在性

利用单调迭代技巧和推广的Mawhin定理得到下述带有p-Laplacian算子的多点边值问题迭代解的存在性,{(Фp(u'))' f(t,u, Tu)=0, 0(≤)t(≤)1,u(0)=q-1∑i=1γiu(δi),u(1)=m-1∑i=1ηiu(ξi),其中Фp(s)=|s|p-2s,p＞1;0＜δi＜1,γi＞0,1(≤)i(≤)q-1;0＜ξi＜1,ηi(≥)0,1(≤)i(≤)m-1且q-1∑i=1γi＜1,m-1∑i=1ηi(≤)1;Tu(t)=∫t0k(t,s)u(s)ds,k(t,s)∈C(I×I,R ).     

TWO POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR BOUNDARY VALUE PROBLEMS

An existence theorem of two positive solutions of the singular BVP1/(p(t))(p(t)y′(t))′+λα(t)f(y(t))=0,t∈(0,1),αy(0)-βp(t)y′(t)=0=γy(1)+δp(t)y′(t)was established by using topological degree theory.     

HLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

We study Hlder continuous solutions for the second order integro-differential equations with infinite delay (P1): u′′(t)+cu′(t)+∫t-∞β(t-s)u′(s)ds+∫t-∞γ(t-s)u(s)ds = Au(t)-∫t-∞δ(t-s)Au(s)ds + f(t)on the line R, where 0 < α < 1, A is a closed operator in a complex Banach space X, c ∈ C is a constant, f ∈ C~α(R,X) and β,γ,δ∈L~1(R+).Under suitable assumptions on the kernels β, γ and δ, we completely characterize the C~α- well-posedness of (P_1) by using operator-valued C~α-Fourier multipliers.     

On a periodic prey-predator system with infinite delays

§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…     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with