Isolated singularity for semilinear elliptic equations

Lei Wei; Zhaosheng Feng

doi:10.3934/dcds.2015.35.3239

Article Contents

2015, Volume 35, Issue 7: 3239-3252. Doi: 10.3934/dcds.2015.35.3239

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Isolated singularity for semilinear elliptic equations

Lei Wei^1, and
Zhaosheng Feng^2,

1.
School of Mathematical and Statistics, Jiangsu Normal University, Xuzhou 221116
2.
Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539

Received: November 30, 2013

Revised: July 31, 2014

Published: May 2017

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Abstract

In this paper, we study a class of semilinear elliptic equations with the Hardy potential. By means of the super-subsolution method and the comparison principle, we explore the existence of a minimal positive solution and a maximal positive solution. Through a scaling technique, we obtain the asymptotic property of positive solutions near the origin. Finally, the nonexistence of a positive solution is proven when the parameter is larger than a critical value.

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Mathematics Subject Classification: 35J61, 35B40.

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References

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