标题： 二维带有奇异权的半线性椭圆方程的分岔图 显示英文标题

标题： Bifurcation diagrams for semilinear elliptic equations with singular weights in two dimensions

摘要： 我们考虑单位球中具有正径向对称权函数的Gelfand问题的径向解的分岔图。 我们处理指数非线性和幂次型非线性。 当权函数为常数时，众所周知，根据维数和高维情况下的幂次指数，分岔曲线表现出三种不同的类型，而在二维情况下，曲线仅表现出一种类型。 在本文中，通过适当选择权函数，我们在二维情况下成功实现了分岔曲线表现出所有三种类型的现象。 特别是，据作者所知，这是首次在二维情况下建立没有拐点的分岔曲线的结果。 显示英文摘要

摘要： We consider the bifurcation diagram of radial solutions for the Gelfand problem with a positive radially symmetric weight in the unit ball. We deal with the exponential nonlinearity and a power-type nonlinearity. When the weight is constant, it is well-known that the bifurcation curve exhibits three different types depending on the dimension and the exponent of power for higher dimensions, while the curve exhibits only one type in two dimensions. In this paper, we succeed in realizing in two dimensions a phenomenon such that the bifurcation curve exhibits all of the three types, by choosing the weight appropriately. In particular, to the best of the author's knowledge, it is the first result to establish in two dimensions the bifurcation curve having no turning points.