1) Leray-Schauder degree
Leray-Schauder度
1.
This paper investigates the existence of solutions for the one dimensional p(t)-Laplacian system multipoint boundary value problems via Leray-Schauder degree.
利用Leray-Schauder度方法研究一维p(t)-Laplace方程组多点边值问题解的存在性。
2.
This article studies the existence of at least three solutions of third-order three-point boundary value problem and get the sufficient conditions of the existence of at least three solutions by use of Leray-Schauder degree theory.
研究了一类三阶三点边值问题的三个解的存在性,应用Leray-Schauder度理论得到了该问题的三个解存在的充分条件。
3.
Our methods are based upon two pairs of lower and upper solutions and Leray-Schauder degree theory.
主要研究四阶三点边值问题,首次应用两对上下解的方法,在假设f(t,u,v,w)满足Nagumo条件下,应用Leray-Schauder度理论,获得了四阶三点边值问题三解的存在性,在以往有关文献中,涉及的都是解的存在性,对高阶非线性多边值问题多解的研究很少。
2) Leray-Schauder degree theory
Leray-Schauder度理论
1.
When boundary value problems withλhave solutions,the existence of one positive solution of singular three-point boundary value problem with p-Laplacian is proved by Leray-Schauder degree theory.
在带λ的边值问题族有解的情况下,通过Leray-Schauder度理论证明所给奇异边值问题正解的存在性。
2.
In this paper we study zero problems of maximal monotone operators with compact perturbations by applying the Leray-Schauder degree theory.
使用Leray-Schauder度理论研究了带紧扰动的极大单调算子的零点问题,获得了一些新的零点定理。
3) Leray-Schauder degree principle
Leray-Schauder度原理
4) Leray-Schauder theorem
Leray-Schauder定理
1.
We use Leray-Schauder theorem to obtain existence and uniqueness theorems for nonlinear nth-order multipoint boundary value problemsu(n)+f(u(n-2))u(n-1)=g(x,u,u′,…,u(n-1))+e(x),u(i)(ηi)=u(n-2)(0)=u(n-2)(1)=0,0≤ηi≤1,i=0,1,…,n-3in uncontinous condition,correspondence results are extended.
利用Leray-Schauder定理研究了非连续条件下的n阶非线性多点边值问题u(n)+f(u(n-2))u(n-1)=g(x,u,u′,…,u(n-1))+e(x),u(i)(ηi)=u(n-2)(0)=u(n-2)(1)=0,0≤η解的存在性和惟一性,推广了已有的相应结果。
5) Leray-Schauder principle
Leray-Schauder原理
1.
The existence of solutions to the singular second-order boundary-value problem x″(t)=f(t,x(t))+e(t),0<t<1;x(0)=0,x(1)=∫01a(t)x(t)dt on C1[0,1) was taken into consideration by using Leray-Schauder principle.
运用Leray-Schauder原理考虑二阶奇异边值问题x″(t)=f(t,x(t),x′(t))+e(t),0
2.
We mainly use Leray-Schauder principle to abtain existence theorems for some classes of nonlinear higher-order two-point boundary value problems.
主要利用Leray-Schauder原理研究了几类高阶非线性两点边值问题解的存在性。
3.
On the base of the increasing nonlinear function and by using Leray-Schauder principle,the existence of the solution of a kind of fourth-order two-point bourdary value problem was discussed.
利用Leray-Schauder原理,在非线性增长条件下,讨论一类四阶两点边值问题的解的存在性。
6) Leray-Schauder theorem
Leray-Schauder原理
1.
Based upon the Leray-Schauder theorem,it is concerned that the singular boundary value problem at the existence of a C~1[0,1) solution x″(t)=f(t,x(t),x′(t))+e(t),t∈(0,1),x′(0)=0,x(1)=kx(η).
运用Leray-Schauder原理考虑了二阶奇异边值问题x″(t)=f(t,x(t),x′(t))+e(t),t∈(0,1),x′(0)=0,x(1)=kx(η)在C1[0,1)上解的存在性。
2.
By using the Leray-Schauder theorem,the existence of solutions for three-point boundary value problems of a class of second order ordinary differential equation is obtained.
运用Leray-Schauder原理,获得了一类二阶非线性常微分方程三点边值问题解的存在性。
3.
By using Leray-Schauder theorem,the optimal sufficient conditions for the existence of the solution of the problemu(4)(t)=f(t,u(t),u″(t)),t∈(0,1)u′(0)=u′(1)=u(0)=u(1)=0are obtained.
应用Leray-Schauder原理,研究四阶两点边值问题u(4)(t)=f(t,u(t),u″(t)),t∈(0,1)u′(0)=u′(1)=u(0)=u(1)=0解的存在性,在两参数非共振条件以及非线性项f满足至多线性增长性条件下给出了此类问题有解存在的最优充分条件,最后举例说明了所获结果。
补充资料：Leray谱序列
Leray谱序列
Leray spactral sequence
hmy谱序列[L”y，曲阁涨月.改‘e;瓜Pec此K印朋、-H盼noc月e八OBaTe月‘”oeT“]，连续映射的谱序列(s伴c七vdlseqUence of a eontinuous rnapPing) 一个将拓扑空间X的取值于可换群层犷的上同调与它在连续映射f:X~Y下的直接象f;(了)的上同调联系起来的谱序列.更确切些，Lemy谱序列的第二项是 五雪，“一H’(Y，f，(·犷))，而它的极限E。是由分次群H’(x，犷)的滤子所决定的双分次群.玫my谱序列可以推广到支集属于特定族的上同调去.J.Lelay于l叫6年(见flJ，121)就局部紧空间和具紧支集上同调的情形，构作了玩ray谱序列. 若犷=A是对应于可换群A的常值层，f是以F为纤维的局部平凡纤维丛的投射，又空间Y为局部可缩的，那么f，(‘犷)是局部常值层·这时项EZ有特别简单的形式. 局部可缩性可以用X，Y，F的其他拓扑条件代替(例如，Y是局部紧的，F是紧的). 利用奇异上同调，对于具有纤维是道路连通的阮n℃纤维化，可以造一个Lel刁y谱序列的相应物，它也具有上述局部平凡纤维丛的玩my谱序列的全部性质(灰n℃谱序列(S耽spec回seq月ence)).对奇异同调，也有相应的谱序列.
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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