Infinite boundary value problems for nonlinear impulsive differential equations with quot; supremum quot 的非线性脉冲微分方程无穷边值问题
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Given a ring , one always takes the supremum of some homological dimension of specified modules to obtain the corresponding global dimension , and to characterize the ring from outside 对于给定的结合环，人们往往通过对其上的一些模的某一种同调维数取上确界而得到环的相应的整体维数，进而从外部刻画出环的特征。
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In this article , we study the infinite boundary value problems for first order nonlinear impulsive differential equations with " supremum " by means of the upper and lower solution method and the monotone iterative technique , and obtain the existence theorems for their extremal solutions 摘要应用上下解方法和单调迭代技术研究了带有上确界的一阶非线性脉冲微分方程无穷边值问题，并获得了其极值解的存在性结果。
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According to the quasi - invariance of the moduli of quadrilaterals under quasiconformal mappings , it is natural to think of approximating the maximal dilatation of the extremal quasiconformal mapping by the ratios of the moduli of quadrilaterals . a key problem is : is it true that the supremum of the ratios of the moduli of quadrilaterals equals the maximal dilatation of the extremal quasiconformal mapping 根据拟共形映射下四边形模的拟不变性，利用四边形模之比来逼近它是人们比较容易想到的方法，但关键的问题是四边形模之比的上确界是否等于极值映射的最大伸缩商
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In this chapter , firstly , we apply a result of [ 20 ] to prove that for a class of quasisymmetric homeomorphisms with substantial boundary points , the maximal dilatation of the extremal quasiconformal extension equals the supremum of the ratios of the moduli of quadrilaterals , which improve the result of [ 148 ] 在本章中，我们首先利用了文[ 20 ]的结果，研究了单位圆周上一类具有本质边界点的拟对称同胚，证明了它的极值拟共形延拓的最大伸缩商等于四边形模之比的上确界，改进了文148的有关结果
