本文選題：預(yù)定平均邊界曲率問(wèn)題 + 無(wú)窮多解　； 參考：《華東師范大學(xué)》2017年碩士論文

【摘要】：預(yù)定邊界平均曲率問(wèn)題是共形幾何中的一類(lèi)重要問(wèn)題。本文主要研究了BN上預(yù)定邊界平均曲率問(wèn)題的等價(jià)方程其中K(x)是RN-1上的有界連續(xù)函數(shù),有一串趨向于正無(wú)窮的嚴(yán)格極大值點(diǎn)zj,并且在每個(gè)極大值點(diǎn)zj的小鄰域內(nèi)有如下形式的展開(kāi)本文通過(guò)有限維約化方法,將求解能量泛函I(u)的臨界點(diǎn)問(wèn)題轉(zhuǎn)化為求解定義在有限維區(qū)域上泛函的臨界點(diǎn)問(wèn)題,從而得到該方程的無(wú)窮多個(gè)正解,且這些解都有兩個(gè)極大值點(diǎn),這兩個(gè)極大值點(diǎn)之間的距離很大。
[Abstract]:The mean curvature problem is an important problem in conformal geometry. In this paper, we study the equivalent equation of the mean curvature problem with predetermined boundary on BN, where Knx) is a bounded continuous function on RN-1. There is a series of strict maximum points zjj which tend to be positive infinity, and there are the following forms of expansion in the small neighborhood of every maximum point zj. In this paper, the finite dimension reduction method is used. The critical point problem for solving the energy functional is transformed into a critical point problem for solving a functional defined in a finite dimensional domain, and the infinite positive solutions of the equation are obtained, all of which have two maximum points. The distance between the two maximum points is very large.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O186.1

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1 周靜;Paneitz問(wèn)題的集中解[D];華中師范大學(xué);2008年

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本文編號(hào)：1913018