Translator Disclaimer
September/October 2015 Self-generated interior blow-up solutions of fractional elliptic equation with absorption
Huyuan Chen, Patricio Felmer, Alexander Quaas
Differential Integral Equations 28(9/10): 839-860 (September/October 2015).

Abstract

In this paper, we study positive solutions to problems involving the fractional Laplacian \begin{equation} \begin{cases} (-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=0,\ \ \ \ & x\in\Omega\setminus\mathcal{C},\\ \ \quad \ u(x)=0,\ & x\in\Omega^c,\\ \displaystyle \lim_{x\in\Omega\setminus\mathcal{C}, \ x\to\mathcal{C}}u(x)=+\infty, \end{cases} \tag*{(0.1)} \end{equation} where $p>1$ and $\Omega$ is an open bounded $C^2$ domain in $\mathbb{R}^N$, $\mathcal{C}\subset \Omega$ is a compact $C^2$ manifold with $N-1$ multiples dimensions and without boundary, the operator $(-\Delta)^{\alpha}$ with $\alpha\in(0,1)$ is the fractional Laplacian. We consider the existence of positive solutions for problem (0.1). Moreover, we further analyze uniqueness, asymptotic behavior and nonexistence.

Citation

Download Citation

Huyuan Chen. Patricio Felmer. Alexander Quaas. "Self-generated interior blow-up solutions of fractional elliptic equation with absorption." Differential Integral Equations 28 (9/10) 839 - 860, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1363.35368
MathSciNet: MR3360722

Subjects:
Primary: 35B40, 35B44, 35R11

Rights: Copyright © 2015 Khayyam Publishing, Inc.

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.28 • No. 9/10 • September/October 2015
Back to Top