论文标题
具有强大潜力的半线性方程的大量解决方案
Large solutions of semilinear equations with Hardy potential
论文作者
论文摘要
我们考虑平滑域中的$-L_μU + f（u）= 0 $的等式，其中$l_μ=δ +μδ{ - 2} $和$δ（x）$表示点$ x $的距离与域边界的距离。非线性项$ f $是正面的，在$（0，\ infty）$上增加和凸，满足了凯勒 - 塞尔曼的条件和一些其他技术假设。尤其是通过权力和指数非线性满足条件。当$μ> 0 $时，我们讨论了大解决方案的存在和唯一性问题。
We consider equations of the form $-L_μu +f(u)=0$ in a smooth domain $Ω$, where $L_μ=Δ+ μδ^{-2}$ and $δ(x)$ denotes the distance of the point $x$ to the boundary of the domain. The nonlinear term $f$ is positive, increasing and convex on $(0,\infty)$, satisfies the Keller-Osserman condition and some additional technical assumptions. The conditions are satisfied, in particular, by power and exponential nonlinearities. We discuss the question of existence and uniqueness of large solutions when $μ>0$.
