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

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[center]A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials
Florica C. Cirstea, "A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials"
2014 | ISBN-10: 0821890220 | 85 pages | PDF | 0,7 MB


In this paper, the author considers semilinear elliptic equations of the form $-\Delta u- \frac{\lambda}u +b(x)\,h(u)=0$ 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.


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Tags: Complete, Classification, Isolated, Singularities, Nonlinear, Elliptic, Equations, Inverse, Square, Potentials

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