Main A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials
A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials cover

A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials

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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 $\Omega\setminus\{0\}$, 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, $\lim_{t\to \infty} h(\xi t)/h(t)=\xi^q$ 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 $t\to \infty$ and $b(x)=|x|^\theta (-\log |x|)^{\alpha_2}$ as $|x|\to 0$, where $\alpha_1$ and $\alpha_2$ are any real numbers
Request Code : ZLIBIO1440706
Categories:
Year:
2014
Publisher:
American Mathematical Society
Language:
English
Pages:
85
ISBN 10:
0821890220
ISBN:
978-0-8218-9022-6,0821890220
Series:
Memoirs of the American Mathematical Society no. 1068

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