دانلود کتاب یک طبقه بندی کامل نقاط تکین جدا شده برای معادلات بیضوی غیر خطی با مربع پتانسیل معکوس

In this paper, the author considers semilinear elliptic equations of the form $-Delta u- frac{lambda}{|x|^2}u +b(x),h(u)=0$ in $Omegasetminus{0}$, where $lambda$ is a parameter with $-infty0$. The author completely classifies the behaviour near zero of all positive solutions of equation (0.1) when $h$ is regularly varying at $infty$ with index $q$ greater than $1$ (that is, $lim_{tto infty} h(xi t)/h(t)=xi^q$ for every $xi>0$). In particular, the author's results apply to equation (0.1) with $h(t)=t^q (log t)^{alpha_1}$ as $tto infty$ and $b(x)=|x|^theta (-log |x|)^{alpha_2}$ as $|x|to 0$, where $alpha_1$ and $alpha_2$ are any real numbers.