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For the non-homogeneous multi-dimensional scalar conservation laws, there is no existence theorem of global weak solution.

关于高维单守恒律方程的研究,对于非齐次的情形,至今还没有得到全局弱解的存在性定理。

It is therefore essential to devise some kind of proper notion of generalized or weak solution.

所以,设计一个合适的广义解或弱解的适当的定义,这是非常重要的,但是一个巧妙的任务。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中,简要介绍了变分法的产生、发展过程,在第二章中我们介绍了有关变分法的一些基本知识,包括Sobolev空间,—△算子,弱解,极小化序列方法和一些极小极大定理,在第三章中我们介绍了非线性项有界或满足次线性条件,以及它满足推广的Ahmad-Lazer-Paul条件时,二阶Hamiltonian系统和半线性椭圆问题的研究历程,最后在第四章中我们证明了本论文的主要定理,并把它应用到第三章的问题中,使得前面的几种共振的情形都可以统一到这个抽象的结果中。

Through studing the weak solution in Sobolev space,its solvability has been proved.

通过在Sobolev 空间中对弱解的讨论,证明了它的可解性。

This is the tendency for water to pass through a membrane separating a weak solution from a strong one.

渗透是一种水通过膜的运动趋势,膜的两面分别是浓溶液和稀溶液。

Firstly, by use of the successive approximation method and a series of classical estimates, the local existence and uniqueness of weak solution are proved.

利用逐次逼近方法和一系列经典的估计,证明了弱解的局部存在性和惟一性。

Free door-to-door offers a full range of intelligent systems engineering weak solution program.

免费上门提供全方位的智能化弱电系统工程的解决方案。

The energy inequality and parabolic monotonici ty inequality is essential for the regularity of a weak solution to this problem .

该问题弱解的能量不等式和抛物单调不等式在证明弱解的正则性时起关键作用。

In this paper,we prove the existence and uniqueness of global weak solution of Non Newton Filtration equation with a kind of nonlinear boundary condition.

证明了一类具有非线性边值条件的非牛顿渗流方程解的存在和唯一性。

In view of the identity, the sufficient conditions of nonexistence of weak solution for two classes of quasilinear probles are obtained.

利用该恒等式,得到了两类拟线性问题弱解不存在的充分性条件。

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Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

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