發(fā)布時(shí)間：2018-10-20 16:02

【摘要】：關(guān)于基爾霍夫的問題最近已經(jīng)被通過很多方法研究,當(dāng)然這些研究大都是在R3的一個(gè)有界區(qū)域上進(jìn)行的.而薛定諤-基爾霍夫的問題也有一些研究,可見有關(guān)基爾霍夫方面的問題是一個(gè)很有意思的課題,換句話說,是一個(gè)很值得繼續(xù)研究并很有潛力發(fā)畏的方向.由于本文各個(gè)部分內(nèi)容的不同,我們將分成三個(gè)部分：第一章,我們主要講一些基礎(chǔ)理論知識(shí).第二章,我們通過對(duì)基爾霍夫方程的靜模擬,對(duì)滿足以下條件：滿足是一個(gè)常數(shù).對(duì)任意記為R3中的勒貝格測(cè)度.這里是一個(gè)正連續(xù)函數(shù)使得是一個(gè)常數(shù).則有無窮解{uK}滿足下列方程：第三章,通過對(duì)條件的分析討論,我們將得到下面的結(jié)論：設(shè)(V1),(f1)—(f4)成立,若0不是的特征值,那么薛定諤-基爾霍夫方程至少有一個(gè)非平凡解u∈X.若(V1)(f1)-(f5)成立,那么這個(gè)薛定諤-基爾霍夫方程有一列解{u。}∈X滿足能量泛函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，

本文編號(hào)：2283649