fold singularity

In this paper,the existence of positive solutions to the following first-order singular periodic boundary value problem is proved by using Green Function and Fixed Point Theorem in cones for problem,u′(t)+ρ2u(t)=f(t,u(t)),0≤t≤2πu(0)=u(2π) where f(t,u) may appear singularity at u=0.

利用格林函数与锥不动点定理证明了奇异一阶微分方程周期边值问题u′(t)+ρ2u(t)=f(t,u(t)),0≤t≤2πu(0)=u(2π)正解的存在性,其中允许f在u=0处具有奇性且常数ρ≠0。

This paper deals with a class of singular Positone boundary value problems.

对一类具有奇性Positone边界值问题进行了研究,利用非线性二择一不动点定理建立了问题正解的3个存在性原则。

On the basis of the cone-fixed point theorem, the present paper deals with the existence of positive solutions to the superlinear second order periodic boundary value problem-u″(t)+ρ 2u(t)=f(t,u(t)), 0≤t≤2π, u(0)=u(2π), u′(0)=u′(2π)where f(t,u) is allowed to be singular at u=0 and superlinear at u=+∞.

利用锥不动点定理证明一个二阶奇异周期边值问题- u″(t) +ρ2 u(t) =f(t,u(t) ) , 0≤ t≤ 2π,u(0 ) =u(2π) , u′(0 ) =u′(2π)正解的存在性 ,其中允许 f在 u=0处具有奇性 ,在 u=+∞处超线性 。

The plot gets more involved.

情节变得更曲折离奇。

That red gold royal gown of 80lbs, about the same weight of herself, only she can bear with it.

那袭八十多磅曲折离奇的烁金豔红宫廷裙褂，同体重差不多，只有她承担得起。

Twist,Tortuousness and Whimsy:On the Plot features,Characterization and Language Artistic Achievements of the "Wu Shuang's Story".

跌宕幽悬 曲折离奇——谈《无双传》的情节特色兼及人物塑造与语言艺术成就

The plot twists and turns, but the ending is the biggest surprise of all.

故事情节迂回曲折，结局令人惊奇。

Moving in or having a zigzag.

曲折的曲折移动的或弯曲的

elbow refractor

折轴反光望远镜;折轴折射望远镜;曲折折光计

Most of his works embodied stories full of twists and turns while his early writings carried an obvious romantic color.

许地山的作品大都故事曲折，早期作品具有明显的浪漫主义传奇色彩。

They walked on through a tunnel into a ravine green with magnificent trees and ablaze with rare flowers. A clear stream welling up where the trees were thickest wound its way through clefts in the rocks.

"说着,进入石洞来.只见佳木茏葱,奇花闪灼,一带清流,从花木深处曲折泻于石隙之下"

We followed the path zigzagging up the steep slope.

我们沿着小径曲曲折折地爬上陡坡。

Flocks of white clouds still float through the mountains today.

两条白线，曲曲折折，是奈河，是汶河。

To wind in a zigzagging course.

弯曲在弯曲的道路上曲折前行

Singularities of Parallels for Hyperbolic Plane Curves

双曲平面曲线的平行曲线的奇点分类

Full of twists and turns;tortuous.

弯弯曲曲的；迂回的充满弯曲和拐弯的；曲折的

The stream snakes its way across the field.

小溪蜿曲折地流过田野。

a wandering river

一条蜿蜒曲折的河流

A cranky mountain road.

一条蜿蜒曲折的山路

weave through the valleys

(路)曲折(蜿蜒)地通过山谷

(cause sth to) become twisted or break under pressure

（使某物）弯曲或折断