Global structure of the solution set for a semilinear elliptic problem related to the Liouville equation on an annulus
Global structure of the solution set for a semilinear elliptic problem related to the Liouville equation on an annulus
复制标题
与环面上的刘维尔方程相关的半线性椭圆问题解集的全局结构
DOI：
10.1007/978-88-470-2841-8_13
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
菅徹
中科院分区：
文献类型：
--
作者：
細谷 昭仁;大西 英博;佐藤 美洋;Tajiri Minako;菅徹
研究了与二维环面上的刘维尔方程相关的半线性椭圆问题。该问题表现为圆环内半径趋于0时刘维尔方程的极限问题，并通过匹配渐近展开法推导出来。我们关心的是分岔图中问题的解集。我们找到包括非径向对称解的显式解，并确定包含这些解的连通分量。因此，我们为刘维尔方程解集的全局结构提供了暗示性证据。
A semilinear elliptic problem related to the Liouville equation on a two-dimensional annulus is studied. The problem appears as the limiting problem of the Liouville equation as the inside radius of the annulus tends to 0, and is derived by the method of matched asymptotic expansions. Our concern is the solution set of the problem in the bifurcation diagram. We find explicit solutions including non-radially symmetric solutions and determine the connected component containing the solutions. As a consequence, we provide a suggestive evidence for the global structure of the solution set of the Liouville equation.