This paper discusses how to teach students"the product of infinite infinitesimals isn t necessarily infinitesimal" in teaching "advanced mathematics" Or "Mathematical Analysis",and the author provides some new original examples which had not been seen in currently available textbook and riches the teaching content.
文章对"无穷多个无穷小的乘积不一定是无穷小"这一知识点在"高等数学"或"数学分析"的教学中如何讲授给学生进行了一些有益的探讨,并给出了一些在现有教科书及参考书中未曾见过的独创的新例子,从而丰富了教学内容。
By means of the variational approach,in a condition weaker than(AR) the existence of infinitely many solutions of fourth-order elliptic equation is discussed.
在比(AR)条件更弱的一类超线性条件之下,利用变分方法讨论了一类超线性四阶椭圆方程的无穷多解的存在性。
The aim of this paper is to discuss the infinitely many solutions of a class of p-biharmonic-like equations on a bounded smooth domain of RN,where 2p>N,and the nonlinearity may not be odd symmetric.
讨论了RN中有界光滑区域上的一类类p-双调和方程的无穷多解问题,其中2p>N,非线性项不必具有奇对称性。
In this paper,we considered the multiple solutions of the following p-Biharmonic-Like problem with 0-Dirichlet boundary value in a bounded domain with smooth boundary:△(a(△u|)△u|△u) = f (x,u), where f (x,u) is a nonlinear odd term.
考虑了类P-双调和方程△((a△up)△up-2△u)=f(x,u)的Dirichlet零边值问题的无穷多解问题,这里的非线性项是奇的,通过验证所定义的泛函满足Cerami条件,从而运用喷泉定理,得到了无穷多个大能量解的存在性。
By considering the following p-Laplace problem of 0-DDirichlet boundary value in a bounded domain of Ω=(0,1)~N:-div(|Du|~(p-2)Du)=g(x,u)+f(x), the existence of multiple solutions in W~_(1,p)_0(Ω) is shown under some assumptions in this paper.
在有界区域Ω=(0,1)N中讨论含非对称形式的p laplace方程-div(|Du|p-2Du)=g(x,u)+f(x)的Dirichlet零边值问题,给出了在一定条件下无穷多解的存在性。
In this paper, the recent achievements of multiple solutions in semilinear ellipic problems and p-Laplacian problems are related.
在更一般的条件下用不同的方法获得了方程无穷多解的存在性结果。
The infinite set of dimensions Dq, singularity of strength α(q) and the fractional dimension f(α) oftwo-frequency quasiperiodic attractor in the quasiperiodically forced circle map are numerically calculated, andthe corresponding figures are given.
用数值计算方法计算了准周期强迫园映象中两频率准周期吸引子的无穷多维数Ｄｑ、奇性强度α（ｑ）与α的点集维数ｆ（α）值，并给出了相应的图线。
The Thinking about the Product of Infinite Infinitesimals;
关于无穷多个无穷小的乘积的一些思考
The integers divide the number line into infinitely many half-open intervals.
整数把数轴分成无穷多个半开区间。
Infinitely periodic solutions for a class second-order Hamiltonian systems
一类二阶Hamiltonian系统的无穷多周期解
Infinitely Many Solutions of a Class of Superlinear P-Laplace equation
一类超线性P-Laplace方程的无穷多解
There are infinitely many real numbers between any two distinct real numbers.
在任何两个实数之间都有无穷多个实数。
Existence of Solutions of Second-order Ordinary Differential Equation Infinite-Point Boundary Value Problems;
二阶常微分方程无穷多点边值问题的可解性
Infinitely Many Solutions for Two Non-cooperative p(x)-Laplacian Elliptic Systems;
两类非合作p（x）-Laplacian椭圆方程组的无穷多解性
Infinitely Many Solutions of p-Laplacian Equation with Nonsymmeteic Disturbing Term;
含有非对称扰动项的P-Laplacian方程的无穷多解问题
Multiple Positive Solutions to a Kind of Second-Order Four-Point Boundary Value Problem;
一类二阶四点边值问题无穷多个正解的存在性
Infinitely Many Subharmonic Solutions for One-dimensional p-sublinear Laplacian Equation
一维p-次线性Laplace方程的无穷多次调和解
The Infinite Multiple Solutions for the p-harmonic Equations with the Navier Boundary Value Conditions
带Navier边值条件的p-调和方程的无穷多解性
The Existence of Infinite Many Solutions to a Hardy Equation with Convex and Concave Nonlinearities
一个带凸凹项的Hardy方程的无穷多解的存在性
They were in countless numbers.
它们的数目多至无穷。
This is a good reminder for all of us. You can never Read this too manytimes!
以下建议非常实用，多看几次，受用无穷！
Chain type channels are not enough and with unlimited potential
连锁型的通路现仍不多、潜力无穷
Poverty has many roots, but the top root is ignorance.
贫穷有许多根源，但最主要的是无知。
Boundaries of the polygon may extend to infinity.
多角形的边界可以延伸到无穷远处。
Justice must not be den to anyone, however poor he may be.
人无论多么穷，都该受到公平的待遇。