存在性定理

We prove the existence of integral solutions for semilinear integrodifferential equations with nonlocal conditions in Banach spaces.

运用预解算子理论和Schauder不动点定理，在Banach空间证明了一类非局部半线性积微分方程积分解的存在性。

This chapter deals with the existence of mild and strong solutions of a nonlinear integrodifferential systems of Sobolev type with nonlocal condition in Banach spaces.

本章在Banach空间中，用算子半群理论以及Schauder不动点定理讨论了一类非线性Sobolev型积分微分方程，在非局部初始条件下，适度解和强解的存在性。

Secondly, by using the Sobolev inequality on the C-C spaces we prove a Fefferman-Phong type lemma. Based on which we provide nonexistence theorems to three kinds of nonlinear subelliptic parabolic equations through a relatively unified method.

其次，利用Carnot-Caratheodory空间上的Sobolev不等式证明了一个Fefferman-Phong型引理，并用比较统一的方法证明了三类非线性次椭圆抛物方程解的不存在性判定定理。

In chapter 3, as a application of fixed point theorems in gauge spaces, by using the results in chapter 2 we study the existence and uniqueness of solution for integral equation of Voletrra type in C.

第三章，作为度规空间中的不动点定理的应用，我们利用第二章中的结果，在C空间中研究了Voletrra型积分方程解的存在性与唯一性。

In Chapter 2, we study the existence of positive solutions for two-point and three-point boundary value problems of nonlinear differential equations.

第一节，运用锥拉伸与锥压缩不动点定理研究二阶三点边值问题正解的存在性。

In section 2, we study the existence of sign-changing solutions of some three-point boundary value problem by the cone theory and the fixed-point index theory.

本文利用不动点指数定理研究了如下两种二阶微分方程多点边值问题变号解的存在性，同时分别得到了一个正解和一个负解。

Firstly in§2.1, by applying the fixed point theorem the existence of positive solutions for second-order three-point boundary value problem is discussed.

第二节，运用不动点定理研究四阶两点边值问题正解的存在性。

In the second chapter we consider the existence of multiple nontrivial solutions for a class of quasilinear elliptic boundary value problems.

在第二章，我们运用下半连续及鞍点定理得到了一类拟线性椭圆边值为体的多重非平凡解的存在性。

By Ricceri's three critical points theorem, the existence of solutions for a class of quasilinear elliptic systems with variational structure was proved and the location of the solutions was also determined.

通过运用Ricceri的一个三临界点定理，讨论了一类具变分结构的拟线性椭圆方程组，获得了多解的存在性，并且给出了解的位置。

By means of relevant methods and theorems in the qualitative theory of differential equations, traveling wave solution of a compound Burgers-Korteweg-de Vries equation is studied.

利用微分方程定性理论的相关方法和定理，对一类复合Burgers-Korteweg-de Vries方程进行研究，获得了方程行波解的存在性和唯一性，并给出了方程行波解的表达式，与此同时，研究了行波解的动力学行为和它们不同解的分岔。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。