1) 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。
2) 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。
3) Leray-Schauder theory
Leray-Schauder原理
1.
Using the Leray-Schauder theory and upper and lower solution method,the existence of solutions for general initial value problem of first order differential equationx′(t)=f(t,x(t)),a.
运用Leray-Schauder原理和上下解方法,讨论了一阶常微分方程广义初值问题x′(t)=f(t,x(t)), a e t∈[0,T],x(0)+∫T0a(t)x(t)dt=c解的存在性。
4) Leray-Schauder degree principle
Leray-Schauder度原理
5) Leray-Schauder fixed point theorem
Leray-Schauder不动点原理
1.
The existence of a time-periodic solution is proved by the Galerkin method,Leray-Schauder fixed point theorem andpriori estimates.
利用伽辽金方法、Leray-Schauder不动点原理和先验估计,证明了在带周期外力扰动和周期边界条件的影响下,非线性发展Ginzburg-Landau方程ut=(l+iα)Δu-(k+iβ)u2u+γ+f的时间周期解,其中f(t,x)是一个关于时间变量t的以ω为周期的函数。
2.
We prove the existence of time-periodic solutions to the Galerkin problem by using Leray-Schauder fixed point theorem.
首先利用Leray-Schauder不动点原理证明Galerkin近似问题有时间周期解,然后利用先验估计和紧致性证明近似解是收敛的,并且其极限就是原来问题的时间周期解。
6) 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。
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.
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