薛定谔—基尔霍夫方程的解及解的存在性和多重性的研究
发布时间：2018-10-20 16:02
【摘要】：关于基尔霍夫的问题最近已经被通过很多方法研究,当然这些研究大都是在R3的一个有界区域上进行的.而薛定谔-基尔霍夫的问题也有一些研究,可见有关基尔霍夫方面的问题是一个很有意思的课题,换句话说,是一个很值得继续研究并很有潜力发畏的方向.由于本文各个部分内容的不同,我们将分成三个部分：第一章,我们主要讲一些基础理论知识.第二章,我们通过对基尔霍夫方程的静模拟,对满足以下条件：满足是一个常数.对任意记为R3中的勒贝格测度.这里是一个正连续函数使得是一个常数.则有无穷解{uK}满足下列方程：第三章,通过对条件的分析讨论,我们将得到下面的结论：设(V1),(f1)—(f4)成立,若0不是的特征值,那么薛定谔-基尔霍夫方程至少有一个非平凡解u∈X.若(V1)(f1)-(f5)成立,那么这个薛定谔-基尔霍夫方程有一列解{u。}∈X满足能量泛函Φ(u。)→+∞.
[Abstract]:The question of Kirchhoff has recently been studied by a number of methods, of course, mostly on a bounded region of R3. And Schrodinger-Kirchhoff's problem has also been studied, which shows that the question of Kirchhoff is an interesting topic, in other words, a direction that is worthy of further study and has great potential. Due to the different contents of each part of this paper, we will divide into three parts: chapter one, we mainly talk about some basic theoretical knowledge. In chapter 2, by static simulation of Kirchhoff equation, we obtain the following conditions: satisfaction is a constant. For any Lebesgue measure denoted as R3. Here is a positive continuous function such that it is a constant. Then the infinite solution {uK} satisfies the following equations: chapter 3, by analyzing the conditions, we get the following conclusion: let (V 1), (f 1)-(f 4) hold, if 0 is not the eigenvalue, Then Schrodinger-Kirchhoff equation has at least one nontrivial solution u 鈭，
本文编号：2283649
[Abstract]:The question of Kirchhoff has recently been studied by a number of methods, of course, mostly on a bounded region of R3. And Schrodinger-Kirchhoff's problem has also been studied, which shows that the question of Kirchhoff is an interesting topic, in other words, a direction that is worthy of further study and has great potential. Due to the different contents of each part of this paper, we will divide into three parts: chapter one, we mainly talk about some basic theoretical knowledge. In chapter 2, by static simulation of Kirchhoff equation, we obtain the following conditions: satisfaction is a constant. For any Lebesgue measure denoted as R3. Here is a positive continuous function such that it is a constant. Then the infinite solution {uK} satisfies the following equations: chapter 3, by analyzing the conditions, we get the following conclusion: let (V 1), (f 1)-(f 4) hold, if 0 is not the eigenvalue, Then Schrodinger-Kirchhoff equation has at least one nontrivial solution u 鈭，
本文编号：2283649
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