具有时滞的n维Liénard型方程调和解的存在性

本文利用迭合度理论研究了具有时滞的n维Lienard型方程调和解的存在性,在对阻尼项不作限制的前提下,给出了存在调和解的条件．     

二阶微分方程奇调和解的存在性

利用度理论研究了二阶Liénard方程奇调和解的存在性和二阶Duffing方程具有偶性和奇性的奇调和解的存在性,改进了一些已有的结果.     

一类带有界回复力非线性Hill型方程的周期解

该文研究了一类带有界回复力的Hill方程的周期解问题.针对权函数为正数的情形,证明了无穷多个次调和解的存在性.当权函数关于时间是偶函数时,证明了无穷多个偶次调和解的存在性和偶次调和解的稠密性分布.     

n维Liénard型方程的调和解

本文讨论有周期扰动的n-维Liónard型方程 +■~2F(x)/■x~2■+G(x)=p(t)的调和解,给出了存在调和解的一系列充分性判据。当G(x)=x~TBx时,给出了存在唯一调和解的条件。     

次线性Duffing系统的多重次调和解

本文证明了，次线性Ｄｕｆｆｉｎｇ系统存在无穷多个高阶次调和解及次调和解列是无界的。     

偏差变元的二阶n-维p-Laplacian方程调和解的存在性

本文研究了一类具偏差变元的二阶n-维p-Laplacian方程调和解的存在性,在对阻尼项不作限制的前提下,利用拓扑度理论得到了存在调和解的新条件,改进了一些已有的结果.     

时间映射和跨共振点的Duffing方程

本文在较弱的条件下证明了跨共振点的Duffing方程至少存在一个调和解和无穷多个次调和解,并在对称情况下给出了对称次调和解的一个稠密性分布定理。主要的讨论建立在对时间映射的分析,并利用由丁伟岳推广的Poincare-Birkhoff 扭转定理。     

具有时滞的n维Liénard型方程的调和解

本文讨论具有周期扰动的n维时滞Liénard型方程()的调和解.给出了存在调和解的若干充分条件,推广了GeWeigao(1991)文中的相关结果.     

具有时滞的n维Lienard型方程的调和解

本文讨论具有周期扰动的ｎ维时滞Ｌｉｅｎａｒｄ型方程ｐ（ｔ）的调和解．给出了存在调和解的若干充分条件,推广了ＧｅＷｅｉｇａｏ（１９９１）文中的相关结果．     

双曲极限环在周期扰动下次调和解的分支

研究了一给定平面自治系统的双曲极限环在周期扰动下m阶次调和解的分支问题,用Poincar啨映射,通过变尺度方法,获得了判别m阶次调和解的存在条件,最后给出了一个实例。     

Affine-periodic solutions for discrete dynamical systems

The paper concerns the existence of affine-periodic solutions for discrete dynamicalsystems. This kind of solutions might be periodic, harmonic, quasi-periodic, even non-periodic.We prove the existence of affine-periodic solutions for discrete dynamical systems by using thetheory of Brouwer degree. As applications, another existence theorem is given via Lyapnovfunction.     

On the harmonic Hopf construction

The harmonic Hopf construction is an equivariant ansatz for harmonic maps between Euclidean spheres. We prove existence of solutions in the case that has been open. Moreover, we show that the harmonic Hopf construction on every bi-eigenmap with at least one large eigenvalue has a countable family of solutions (if it has one).

     

Generalized Harmonic Functions and the Dewetting of Thin Films

This paper describes the solvability of Dirichlet problems for Laplace's equation when the boundary data is not smooth enough for the existence of a weak solution in H¹Ω. Scales of spaces of harmonic functions and of boundary traces are defined and the solutions are characterized as limits of classical harmonic functions in special norms. The generalized harmonic functions, and their norms, are defined using series expansions involving harmonic Steklov eigenfunctions on the domain. It is shown that the usual trace operator has a continuous extension to an isometric isomorphism of specific spaces. This provides a characterization of the generalized solutions of harmonic Dirichlet problems. Numerical simulations of a model problem are described. This problem is related to the dewetting of thin films and the associated phenomenology is described.     

一类超线性Hill型对称碰撞方程的周期运动

本文考虑一类超线性Hill型对称碰撞方程的对称碰撞周期解的存在性、重性和分布问题.通过坐标变换的方法把碰撞相平面转化为全平面进行研究,在一类关于时间映射的超线性条件下证明有外力方程无穷多个对称碰撞调和解和对称碰撞次调和解的存在性;同时研究在没有外力时方程的对称碰撞周期解的稠密性分布.本文还给出对称碰撞方程对称碰撞周期解存在的充分条件.     

典型域的调和分析和复Clifford分析

本文利用华罗庚、陆启铿关于多复变函数论中典型域的调和分析研究复Ｃｌｉｆ－ｆｏｒｄ分析中（四种）典型域的调和分析,讨论了两个相应边值问题正则解的存在（唯一）性及其积分表达式．     

A perturbation theory for the discrete harmonic oscillator equation

This work deals with the existence, uniqueness and stability of solutions for the semilinear discrete harmonic oscillator equation on Banach spaces by using recent characterization of maximal regularity for a best difference approximation of the discrete harmonic oscillator equation.     

Global existence and blow-up for harmonic map heat flow

For degree-one equivariant maps on bounded domains, the question of finite-time blow-up vs. global existence of solutions to the harmonic map heat flow has been well studied. In this paper we study the Cauchy problem for degree-m equivariant harmonic map heat flow from (2+1)-dimensional space-time into the 2-sphere with initial energy close to the energy of harmonic maps. It is proved that solutions are globally smooth for m?4, whereas for m=1, we show that finite-time singularities can form for this class of data.