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January/February 2014 Limiting behavior of solutions to an equation with the fractional Laplacian
Xiaoli Chen, Jianfu Yang
Differential Integral Equations 27(1/2): 157-179 (January/February 2014).

Abstract

In this paper, we investigate the limiting behavior of solutions $u_p$ of the following subcritical problem \begin{equation}\label{eq:0.1} (-\Delta)^{\frac \alpha 2} u = |x|^\beta u ^ {p-1},\quad u > 0, \quad x\in\Omega ;\quad u = 0,\quad x \in \partial \Omega \end{equation} as $p$ tending to the critical exponent $2^{*}_{\alpha}$, where $\Omega$ is the unit ball in $\mathbb{R}^n$ centered at the origin, and $\beta>0,0 <\alpha <2,\ 2 < p <2^{*}_{\alpha}=\frac{2N}{N-\alpha}$. We show that $u_p$ concentrates on a point on the boundary of the domain as $p\to 2^{*}_{\alpha}$.

Citation

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Xiaoli Chen. Jianfu Yang. "Limiting behavior of solutions to an equation with the fractional Laplacian." Differential Integral Equations 27 (1/2) 157 - 179, January/February 2014.

Information

Published: January/February 2014
First available in Project Euclid: 12 November 2013

zbMATH: 1313.35084
MathSciNet: MR3161600

Subjects:
Primary: 35B45, 35J25, 35J70, 47G30

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 1/2 • January/February 2014
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