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1.
本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果 相似文献
2.
E. P. Dolzhenko 《Mathematical Notes》1996,60(2):130-136
Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))2. LetH(x) be an arbitrary primitive of 1/h
–1(x). Note that the functionH
–1
x is positive and increasing on (–, +),H
–1 0 asx– andH
–1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000. 相似文献
3.
The work of the author in measure and integration is based on new inner and outer envelope formations, which replace the traditional Carathéodory outer measure and certain simple suprema and infima. The new formations lead to essential improvements in both the extent and the adequacy of the basic results. However, they did not find an entrance into the recent textbook literature. The present paper seeks to demonstrate their power with the examples of the basic inner and outer extension and representation theorems for set functions and functionals. 相似文献
4.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
5.
Let f(z) be a normalized convex (starlike) function on the unit disc D. Let , where z=(z1,z2,…,zn), z1∈D, , pi?1, i=2,…,n, are real numbers. In this note, we prove that Φ(f)(z)=(f(z1),f′(z1)1/p2z2,…,f′(z1)1/pnzn) is a normalized convex (starlike) mapping on Ω, where we choose the power function such that (f′(z1))1/pi|z1=0=1, i=2,…,n. Some other related results are proved. 相似文献
6.
7.
The main aim of this paper is to establish an Ostrowski type inequality on H-type groups using the L∞ norm of the horizontal gradient. The work has been motivated by the work of Anastassiou and Goldstein in [G.A. Anastassiou, J.A. Goldstein, Higher order Ostrowski type inequalities over Euclidean domains, J. Math. Anal. Appl. 337 (2008) 962-968]. 相似文献
8.
The birth, raise, development and fortunes of a fundamental theory in thermodynamics, the axiomatic thermodynamics, a creation of Constantin Carathéodory, is thoroughly presented together with a summary of Carathéodory's biography. Axiomatic thermodynamics is centered around some interesting properties of Pfaffian differential equations, which are here introduced and used for some well-known cases in thermodynamics. 相似文献
9.
We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte–Carlo method for integration problems. 相似文献
10.