1) nonlinear functional analysis
非线性泛函分析
1.
Since the concept of locally fine point, which is the generalized regular point, was introduced, many problems in nonlinear functional analysis have been solved, such as the conjugacy problem, the rank theorem in advanced calculus and so on.
非线性泛函分析中一个著名的结果是 f的正则点全体是 E中的一个开子集。
2.
In this paper some new advances in nonlinear functional analysis obtained by our research group are summarized.
概述了本课题组在非线性泛函分析方面所获得的一些新进展。
2) methods of nonlinear functional analysis
非线性泛函分析方法
3) general principle on ordered sets in nonlinear functional analysis
非线性泛函分析序集一般原理
1.
The study for the general principle on ordered sets in nonlinear functional analysis and its applications is an important problem in nonlinear functional analysis.
非线性泛函分析序集一般原理及其应用的研究是非线性泛函分析的重要研究课题。
4) nonlinear functional differential equation
非线性泛函微分方程
1.
Boundness of second order nonlinear functional differential equations;
一类二阶非线性泛函微分方程解的有界性
2.
Oscillatory and asymptotic behavior of solutions of the second order nonlinear functional differential equation(a(t)(y (t)σ)+q(t)f(y(τ(t))g(y (t))=0,t≥t0 are considered, where σ is a positive quotient ofeven over odd integers.
研究了二阶非线性泛函微分方程(n(t)(y'(t))σ)+q(t)f(y(τ(t))g(y'(t))=0,t≥t0解的振动性 与渐近性,其中σ是一个偶数与奇数的正商时,所得的结果是全新的。
3.
The general nonlinear functional differential equations with infinite delay was investigated.
研究一般的具有无穷时滞的非线性泛函微分方程。
5) nonlinear functional differential equations
非线性泛函微分方程
1.
Boundedness of second-order nonlinear functional differential equations;
关于二阶非线性泛函微分方程的有界性
2.
Considers boundedness of solutions of nonlinear functional differential equations,obtains several new sufficient criterion.
对一类非线性泛函微分方程解的有界性进行探讨,得到了几个新的判别法则。
6) nonlinear functional difference equation
非线性泛函差分方程
1.
The existence of positive solutions for boundary value problem of a nonlinear functional difference equation with p-Laplacian operator is investigated, where Φp(u) = |u|p-2u, p > 1, (?)(0) = 0, C+ = {(?) :(?) C, (?)(k)≥ 0, k ∈ [-(?),0]}.
作者研究下述的p-Laplace型非线性泛函差分方程边值问题正解和多重正解的存在性,得到相应的充分条件,其中Φp(u)=|u|p-2u,P>1,(?)(0)= 0,C+={(?):(?)∈ C,(?)(k)≥0,k∈[-r,0])。
2.
The existence of multiple positive periodic solutions to nonlinear functional difference equation is considered by using the Leggett-Williams fixed point theorem,and three positive periodic solutions of this problem are obtained.
利用Legett-Williams不动点定理对一类非线性泛函差分方程多个周期正解的存在性进行了讨论,得到该问题3个周期正解的充分条件。
补充资料：非线性泛函分析
非线性泛函分析
non-linear functional analysis
非线性泛函分析I朋Jil蓝，r为.甫OI趁1 al司砰如;讹皿此亚-。。益中扮二”“o。~“益叨“31 泛函分析(几川ctional anal郊is)的一个分支，研究无穷维向量空间之间的非线性映射(算子，见非线性算子(non刁泊口r oPemtor))和某些非线性空间类及其映射，非线性泛函分析的基本部分如下: l)Banach空间、拓扑向量空间和某些更一般空间之间的非线性映射的微分学，包括关于可微映射局部反演的定理和隐函数定理. 2)寻求从一个特定的无穷维空间到另一个空间的非线性算子的作用条件，如连续性、紧性的条件. 3)对各种不同类非线性算子(收缩的(con匕通c-硫)、紧的、压缩的(compressing)、单调的以及其他)的不动点原理;这些原理在各种非线性方程解的存在性证明中的应用. 4)研究赋予序向量空间结构的空间中的非线性算子，如单调的、凹的、凸的、有单调弱函数的以及其他的算子. 5)无穷维向量空间中非线性算子的谱性质的研究(分歧点、本征向量的连续分支等等). 6)非线性算子方程的逼近解. 7)局部线性的空间和E以nach流形的研究—整体分析(咖回analysis). 8)非线性泛函极值的研究和研究非线性算子的变分方法.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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