论文标题
通过分叉理论，奇异椭圆问题的某些存在结果
Some Existence Results for a Singular Elliptic Problem via Bifurcation Theory
论文作者
论文摘要
我们使用变异方法研究了一个半线性椭圆形问题，其类型为$ g（u）= - u^{ - 1} $的单数非线性项。请注意，负符号很重要，因为Euler-Lagrange功能中的相应项是凹面的。与凸情况相反，由于功率为$ -1 $，因此没有解决问题问题的解决方案。因此，我们研究了Neumann问题，并证明了从恒定溶液中分叉的溶液的局部存在。在径向的情况下，我们表明两个分叉分支之一是全局且无限的，我们发现其不可症行为。
We study a semilinear elliptic problem with a singular nonlinear term of the type $g(u)=-u^{-1}$, using a variational approach. Note that the minus sign is important since the corresponding term in the Euler-Lagrange functional is concave. Contrary to the convex case there are no solutions for the Dirichlet problem, due to the power being $-1$. We therefore study the Neumann problem and prove a local existence result for solutions bifurcating from constant solutions. In the radial case we show that one of the two bifurcation branches is global and unbounded, and we find its asympotic behaviour.
